Controller Parameters Dependence on Model Information Through Dimensional Analysis
|
|
- Darren Robertson
- 6 years ago
- Views:
Transcription
1 Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference Shanghai, PR China, December 16-18, 2009 WeBIn49 Controller Parameters Dependence on Model Information hrough Dimensional Analysis P Balaguer, A Ibeas, C Pedret and S Alcántara Abstract In this article we make use of dimensional analysis in order to investigate the controller parameters dependence on model information ie model parameters he objective is to relate the influence that each model parameter has on each controller parameter In order to accomplish this goal the model transfer function is first analyzed using dimensional analysis and characterized by means of of dimensionless numbers Secondly each controller parameter is related with the model parameters As a result it is derived the underlaying structure that any homogeneous tuning rule must follow he general results are particularized for PID control of first order and second order systems he results can be applied to PID tuning and PID tuning rules comparison I INRODUCION Dimensional analysis [1] is a well known theory applied to physical problems which permits a variety of important results such as i to understand the physical phenomenon, not only the depending quantities but also their relations, ii to represent results in a more compact way by means of dimensionless numbers and iii to generalize experimental results, thus reducing the experimental requirements Control theory can beneficiate from dimensional analysis in a wide variety of ways as can be seen from the bibliography In [2] dimensional analysis is explicitly presented as a theory to be used in control theory related problems In particular dimensional analysis is used to define systems equivalence and to relate system sensitivity to dimensional concepts From a practical point of view dimensionless models of vehicle dynamics are derived and used for controller synthesis In [6] the Buckingham Π theorem is used in order to represent the PID controller parameters of first order plus dead time FOPD model by means of dimensionless numbers, with the aim of performing a numerical optimization of the tuning parameters Practical advances in control design are proposed in [3] In particular it is shown that by means of dimensional analysis it is possible to reduce the scheduling parameters of gain scheduling controllers, thus reducing the analysis and design complexity Dimensional analysis is also used to dump uncertainty representation in dimensionless parameters, what may lead to less conservative results he financial support received from the Spanish CIC programme under grants DPI is greatly recognized P Balaguer is with the Department of Industrial Systems Engineering and Design, Universitat Jaume I de Castelló, Castelló, Spain pbalague@esidujies A Ibeas, C Pedret and S Alcántara are with the Department of elecommunication and Systems Engineering, Autonomous University of Barcelona, Barcelona, Spain Recently, in [5] it is studied the physical dimensions of matrices in state-space models by means of dimensional analysis Moreover, throughout the control bibliography, it is interesting to note that dimensional analysis results are used, although not stated explicitly, in order to tackle some control issues For example in [4] dimensionless parameters of FOPD model are used to compare distinct autotuning methods From the previous review we can see that dimensional analysis permits to tackle distinct control theory issues Although it has been mainly applied to identification and modeling of systems and systems uncertainty, the potential results of dimensional analysis related to controller design and controller comparison seems to have received less attention In this article we apply dimensional analysis on the transfer function framework in order to determine the structural relation among model parameters and controller parameters It is shown that an underlaying structure in fact exists he main result is obtained by firstly representing the transfer function by means of dimensionless numbers, in such a way that the transfer function behavior is characterized using a reduced set of dimensionless parameters he following questions are answered: i Which are the physical dimensions of the transfer function parameters?, ii Is it possible to reduce the number of transfer function parameters by means of dimensionless numbers? If the answer is affirmative, how many parameters can be reduced?, iii What is a proper system of units for the transfer function parameters? Next, on the basis of the preceding results, the dependence of controller parameters on the transfer function dimensionless numbers is established In particular the following questions are answered: i What is the relationship among the controller parameters and the plant model parameters?, ii Do all the model parameters affect in the same way all the controller parameters? and iii Is it possible to state these relationships in a more compact way by means of dimensionless numbers? Finally the general results obtained are particularized for PID control of FOPD and second order models in order to show the practical benefits of the results obtained In particular the results obtained are useful for comparing PID tuning methods as the characterization of controllers and models by means of dimensionless numbers allows the reduction of parameters in the comparison procedure ie the dimensionless number / he contributions of the article are organized as follows /09/$ IEEE 1914
2 WeBIn49 In Section II the basic concepts of dimensional analysis are reviewed Next it is shown in Section III that transfer functions can be represented by means of a reduced set of dimensionless numbers In Section IV it is analyzed the controller parameters dependence on transfer function dimensionless numbers Finally the theoretical results obtained in the preceding Sections are applied to PID control of first and second order systems II DIMENSIONAL ANALSIS Dimensional Analysis [1] is a technique used extensively in physic problems eg fluid dynamics he idea on which dimensional analysis is based is that physical laws are dimensionally homogeneous ie do not depend on the choice of any basic units of measurement, that is the law is valid in any system of dimensions his leads to the fact that functions expressing physical laws have a fundamental property called generalized homogeneity or symmetry his property allows the number of function arguments to be reduced, therefore making the dependence simpler Following we briefly review the fundamental concepts of dimensional analysis and state the fundamental Buckingham Π heorem II-A Physical quantities, Units and Dimensions When we refer to the fact that the length of a cable is 5 meters we are stating the magnitude of a physical quantity However, we could also say that the cable length is 5000 millimeters he only difference being in the units used to describe the physical quantity We then have that: Physical quantity = numerical value Unit 1 hus in both cases we are referring to the same physical quantity ie the cable length is constant, being the only difference the numerical value due to the difference in units eg meters Vs millimeters On the other hand, in both cases we are describing a length he dimension is defined as a qualitative description of a sensory perception of a physical entity It is clear that in both cases we are dealing with the same dimensions We write the dimensions of a quantity φ between square brackets, that is [φ] For example, the quantity lc that describes the length of a cable has length dimensions ie L, that is [lc] = L On the other hand, the velocity dimension is [v] = L 1 where is time dimension he systems of units is the set of fundamental units sufficient for measuring the properties of the class of phenomena under consideration For example in order to study the dynamics of mechanical systems, one system of units could be mass, length and time ie M,L and and a different system of units could be length, force and time ie L,F and However both systems of units are equally valid to study the mechanical system It is necessary to stress that the dimensions are defined by the systems of units employed Finally the concept of independent dimensions is introduced Given a set of quantities, these quantities are said to have independent dimensions if none of these quantities have dimensions which can be represented in terms of a product of powers of the dimensions of the remaining quantities For example, density [ρ]=ml 3, velocity [v]=l 1 and force [f]=ml 2 have independent dimensions In fact there are no x and y that accomplish, for example, the following equation: II-B Buckingham Π heorem [ρ] = [v] x [f] y 2 he Buckingham Π heorem [1] states that if some governed parameter a is a function of n governing parameters, that is: a = fa 1,, a k, a k+1,, a n 3 in such a way that only the set of k parameters given by a 1,, a k have independent dimensions, then there exists n k independent dimensionless parameters Π j j [1, n k] such that the following relation can be established: Π = ΦΠ 1,, Π n k 4 Each one of the dimensionless numbers related with the dependent governing parameters is given by: Π j = a k+j a pj 1 arj k where the exponents p j r j are chosen such that the parameter Π j is dimensionless he dimensionless number related with the governed parameter is: a Π = a p 1 ar k Note that there are n k dimensionless numbers related with each one of the n k dependent governing parameters ie Π j j [1, n k], plus one dimensionless number related with the governed parameter a ie Π As a result the function f equivalently the governed parameter as a = fa 1,,a n can be written in terms of a function Φ of smaller number of variables in the following form: III 5 6 fa 1,, a n = a p 1 ar k ΦΠ 1,, Π n k 7 RANSFER FUNCION DIMENSIONAL ANALSIS In this section we characterize the transfer function by means of dimensional analysis theory he objective is to express a given transfer function by means of dimensionless numbers hus we are able to represent the transfer function information in the most compact way In order to express a transfer function by means of dimensionless numbers, first we find the dimensions of the transfer function parameters Secondly a suitable system of units for transfer function parameters is defined 1915
3 WeBIn49 III-A Analysis of ransfer Function Parameters Dimension he transfer function of a system described by a linear time invariant differential equation is defined as the quotient between the Laplace transform of the output and the Laplace transform of the input under the assumption of zero initial conditions In order to apply the Buckingham Π heorem to a transfer function, it is necessary to know the dimensions of the transfer function parameters his is shown by the following lemma: Lemma 1: Consider a generic transfer function Gs in pole-zero form with c Z and Gs = Ks cg zs g p s e s 8 g z s = g p s = z zj s + 1 j=1 p pi s + 1 i=1 with the following transfer function parameters K, zj, pi and satisfying p z c 0 Note that multiple complex conjugate poles and zeros are also allowed by appropriate complex values of the terms pi and zj hen the sets { pi } and { zj } must be closed under complex conjugation he dimensions of the transfer function parameters are: [K] = U 1 c [ pi ] = [ zj ] = [] = where is the output dimension, U the input dimension and the time dimension Proof: he result of the lemma 1 follows from the following facts First note that [g z s] = 1, that is, dimensionless In fact the dimensions of zj are time dimensions ie they are time constants, thus [ zj ] = On the other hand, the dimensions of the s operator are [s] = 1 It can be seen either in the time domain where the s operator is transformed to operator p defined as p = d/dt or in the frequency domain where s is transformed to jω hus each product zl s yields a dimensionless number he same reasoning applies to g p s and e s Furthermore the dimensions of the transfer function are [Gs] = U 1 As a conclusion of the above analysis it results that [Gs] = [Ks c ], or equivalently [K] = [Gs][s c ] 1 which yields: [K] = U 1 c 9 As a result, the system of units required to study the inputoutput relation given by a transfer function is U ie output dimension, input dimension and time dimension In fact any variable or parameter dimensions can be obtained by a combination of the U dimensions III-B ransfer Function Dimensionless Numbers In this section we make use of the Buckingham Π theorem presented in Section II in order to characterize the transfer function by means of dimensionless numbers As a result we obtain the minimum number of dimensionless numbers required to characterize a transfer function he number of dimensionless numbers is equal to n k where n is the number of governing parameters and k is the number of parameters which have independent dimensions We can consider the following situations regarding the number of physical quantities n considered in the relationship and the number of independent dimensions k: n > k: In this case the number of quantities n appearing in the relating equation is greater than the independent dimensions k As a result we can find n k dimensionless numbers than equivalently relate the above relation n = k: In this case the number of physical quantities equals the number of independent dimensions then n k = 0, so there are no dimensionless numbers n < k: In this case the number of quantities n is less than the number of independent dimensions k his case is not physically possible as the resulting equation is no longer homogenous We now study the number of dimensionless numbers that can be derived from a general transfer function presented in 8 In order to accomplish this goal, it is necessary to calculate the number of governing variables n and the number of variables with independent dimensions k First of all we divide the parameters in three groups: 1 Signals: the output y and the input u 2 ransfer Function parameters: K, zj, pi, and 3 Frequency variable: s If we consider the output as the governed variable, we have: 1916 y = fk,, p1,, pp, z1,, zz, s, u 10 he number of parameters can be calculated as follows: y: he output of a transfer consists of only one parameter, that is #y=1 ie # refers to cardinality u: he input also consists of one parameter then #u=1; K: he system gain is again another single parameter #K=1 : he system delay quantity #=1 if there is time delay In case there is not time delay, #=0 p: he system number of poles with associated parameter is given by p In fact, if c < 0 there are c poles at the origin but with no associated parameter z: he system number of zeros with associated parameter is given by z If c > 0 there are c zeros at the origin but with no associated parameter s: he complex variable is also a parameter governing the output, then #s=1
4 WeBIn49 hen given the relation s = GsUs we find that the number of governing quantities we consider y the governed quantity is given by: n = #u + #K + # + p + z + #s 11 Considering a SISO system we have #u=#k=1 Moreover #s=1 hen it follows that n=3+# +p+z On the other hand as derived in the preceding section, we have that the fundamental system units U he number of governing parameters with independent dimensions is k=3 his is easily seen by considering the input [u] = U, the gain [K] = U 1 c and any other governing parameter, as the rest of them have time dimensions As a result, given any relation described by any transfer function Gs we can expect the following number of dimensionless numbers: n k = 3 + # + m + n 3 = # + p + z 12 hus, we can see that the number of dimensionless numbers is a function of the time parameters, that is the delay and the number of poles and zeros of the transfer function III-C Examples Example 1: Consider a first order system plus time delay: s = Ke s Us 13 s + 1 Firstly we state the governed parameter and the governing parameters hese are: = fu, K,,, s 14 he number of dimensionless numbers is n k = # + p+z In the FOPD case we have that #=1, #p=1 and #z=0, thus n-k=2 As a result we have two dimensionless number: Π 1 =, Π 2 = s 15 Note that the dimensionless numbers are not unique as / and s are also valid here is always an extra dimensionless number related with the governed variable, in this case: Π = K 1 y u 16 hen we have the following relationship Π = ΦΠ 1, Π 2, which can also be written as: = KUΦ, s 17 with the function Φ given by: KU = 1 Π e Π1Π2 18 what can be easily shown by direct substitution In the rest of the article we use the following more meaningful notation to refer to each dimensionless number: yielding finally = Π 1 =, s = Π 2 = s 19 KU = 1 e s 20 s + 1 Example 2: Consider now a second order system without time delay, that is: s = K Us 21 s s + 1 he relations among quantities considered is: = fu, K,, 2, s 22 he number of dimensionless numbers is n k = # +p+ z Now we have that #=0, #p=2 and #z=0, thus the number of dimensionless numbers is again n-k=2 he dimensionless numbers are: Π 1 = 2, Π 2 = s = s 23 he dimensionless number related with the governed variable is the same as the example before, so we have: = KUΦ, s 24 with function Φ given by KU = 1 s + 1Π 1 s Example 3: Consider now a second order system with time delay, that is: s = Ke s Us 26 s s + 1 he relations among quantities considered is: = fu, K,,, 2, s 27 he number of dimensionless numbers is n k = # + p + z In this case we have that #=1, #p=2 and #z=0, thus the number of dimensionless numbers is now n-k=3 he dimensionless number are: Π 1 =, Π 2 = 2, Π 3 = s 28 he dimensionless number related with the governed variable is the same as the example before, so we have: = KUΦ, 2, s 29 with function Φ given by KU = e Π1 s s + 1Π 2 s
5 WeBIn49 IV CONROLLER PARAMEERS DEPENDENCE ON DIMENSIONLESS NUMBERS In this section we apply the dimensional analysis theory in order to analyze the controller parameters dependence on the model transfer function parameters We then consider a generic controller Cs given by: with p Z and Cs = K c s q gc z s g c p s 31 zc gz c s = zj c s + 1 g c ps = j=1 pc pis c + 1 i=1 with the following transfer function parameters K c, zj c and pi c he relative order of the system is pc zc q 0 Note that complex poles and zeros are also allowed by appropriate complex values of the terms pi c and zj c In this case, the sets {pi c } and { zj c } must be closed under complex conjugation hen we are faced with the problem of finding the controller parameters dependence on the model parameters, that is: K c = f 1 K,, p1,, pp, z1,, zz 32 c p1 = f 2 K,, p1,, pp, z1,, zz 33 c ppc = f pc+1 K,, p1,, pp, z1,, zz 34 c z1 = f pc+2 K,, p1,, pp, z1,, zz 35 c zzc = f pc+zc+1 K,, p1,, pp, z1,, zz 36 Remark 1 Note that the governing parameters of each one of the controller parameters is a subset of the governing parameters of the system output as can be seen in equation 10 In fact, the controller parameters do not depend on the input u and on the complex variable s Moreover note that in equation 10 the parameters K and u, due to their dimensions, only affect the governed variable y Remark 2 he governing parameters on equations only have two distinct dimensions, the gain dimension K and the time dimension Moreover there is just one parameter with gain dimension, the transfer function gain K It then follows, due to dimensional homogeneity, that the gain can not appear in the rest of the governing variables all with time dimension in order to make them dimensionless In fact the only parameter that can be made dimensionless by means of the model gain K is the controller gain K c From the above remarks it can be seen that each one of the controller parameters ie governed variables are a function of n k 1 dimensionless numbers hese dimensionless numbers ie Π 1,, Π n k 1 are the ones generated from all transfer function time parameters ie, p1,, pp, z1,, zz As a result we can write KK c = Φ 1 Π 1,, Π n k 1 p1 c = Φ 2 Π 1,, Π n k 1 c ppc z1 c c zzc = Φ pc+1 Π 1,, Π n k 1 = Φ pc+2 Π 1,, Π n k 1 = Φ pc+zc+1 Π 1,, Π n k 1 Note that each one of the controller time constants are divided by his is so because in order to form the dimensionless numbers Π 1,, Π n k 1, the governing parameter was chosen to be the one forming the base of parameters with independent dimension However this selection is arbitrary In the following we particularize this general result for PID controllers of FOPD models and SOPD models V APPLICAION O PID CONROL In what follows we apply the general results stated in Section IV to two distinct model plants to be controlled with PID control V-A First order plus time delay systems In this section we tackle the problem of the PID controller parameter dependence on a FOPD model, with transfer function Gs given by: Gs = Ke s s Recall from example 1 that in this case there is just one dimensionless number related with the transfer function time parameters, which is As a result we have that KK c = Φ 1 i = Φ 2 d = Φ 3 hus, the controller gain depends in an inverse way on the process gain and on an arbitrary function Φ which defines the tuning rule of the dimensionless parameter / he integral time and the derivative time do not depend on the model gain K but are an arbitrary function of the dimensionless parameter / 1918
6 WeBIn49 V-B Second order plus time delay systems In this section we study the PID controller parameters dependence on the second order model plus delay given by: Gs = Ke s s s aking the first time constant as the independent dimension variable we have find the following dimensionless numbers of the transfer function time parameters and hen the controller parameters are obtained as: K c = K 1 Φ 1, 1 i = Φ 2, d = Φ 3, As a result, an equivalent relation as the one obtained in the preceding case is obtained However now the functions Φ i i [1, 2, 3] defining each one of the controller parameters is a function of two dimensionless variables V-C hird order systems In this section we study the PID controller parameters dependence on the third order system given by: Gs = K s s s aking the first time constant as the independent dimension variable we have find the following dimensionless numbers of the transfer function time parameters and 3 hen the controller parameters are obtained as: K c = K 1 Φ 1, 3 i = Φ 2, 3 d = Φ 3, 3 We can see that the controller parameters are again a function of two dimensionless parameters VI APPLICAION EXAMPLE In this section we compare Pade approximations of time delay in FOPD models as the one presented by equation 20 By straightforward calculation the transfer function of the dimensionless approximation error Ē s = G s Ĝ s for a first order Pade approximation is given by Ē s = 1 s + 1 e s 2 s 1 2 s where Ē s is the normalized error transfer function defined s Ŷ s as KU s, with s the FOPD output, Ŷ s the output of the approximate model, U s the model input and K the FOPD gain s is the normalized laplace variable defined as s = s, with the FOPD time constant is the dimensionless time delay defined as = / It can be seen that the normalized error transfer function is a function of just one parameter, the dimensionless time delay As a result the H norm of normalized error transfer function Ē s can be calculated for distinct Pade approximation orders as it is shown in Figure 1 Ē s st Order Pade Approximation 2nd Order Pade Approximation 3rd Order Pade Approximation 4th Order Pade Approximation Ē s / Fig 1 Comparison of Pade Approximations of several Orders VII CONCLUSIONS In this article we have used dimensional analysis to investigate two important aspects of control theory On the one hand it has been established that given a general transfer function, it is possible to characterize it by means of dimensionless numbers he number of dimensionless numbers obtained are equal to the transfer function time parameters On the other hand, dimensional analysis has been used to determine the controller parameters dependence on the model information ie model parameters hese results are general and of interest in order to characterize plant behaviour for analysis purposes as well as to derive PID tuning rules REFERENCES [1] G I Barenblatt Dimensional Analysis Gordon and Breach Science Publishers, 1987 [2] Sean Brennan On Size and Control: he Use of Dimensional Analysis in Controller Design PhD thesis, University of Illinois at Urbana- Champaign, 2002 [3] Haftay Hailu Dimensional ransformation: A Novel Method for Gain Scheduling and Robust Control PhD thesis, he Pennsylvania State University, 2006 [4] A Leva Comparative study of model-based PID autotuning methods In American Control Conference, 2007 [5] H J Palanthandalam-Madapusi, D S Berstein, and R Venugopal Dimensional analysis of matrices IEEE Control Systems Magazine, December: , 2007 [6] S avakoli and M avakoli Optimal tuning of PID controllers for first order plus time delay models using dimensional analysis In International Conference on Control and Automation,
IMC based automatic tuning method for PID controllers in a Smith predictor configuration
Computers and Chemical Engineering 28 (2004) 281 290 IMC based automatic tuning method for PID controllers in a Smith predictor configuration Ibrahim Kaya Department of Electrical and Electronics Engineering,
More informationLecture 5: Linear Systems. Transfer functions. Frequency Domain Analysis. Basic Control Design.
ISS0031 Modeling and Identification Lecture 5: Linear Systems. Transfer functions. Frequency Domain Analysis. Basic Control Design. Aleksei Tepljakov, Ph.D. September 30, 2015 Linear Dynamic Systems Definition
More informationISA-PID Controller Tuning: A combined min-max / ISE approach
Proceedings of the 26 IEEE International Conference on Control Applications Munich, Germany, October 4-6, 26 FrB11.2 ISA-PID Controller Tuning: A combined min-max / ISE approach Ramon Vilanova, Pedro Balaguer
More informationCHAPTER 7 FRACTIONAL ORDER SYSTEMS WITH FRACTIONAL ORDER CONTROLLERS
9 CHAPTER 7 FRACTIONAL ORDER SYSTEMS WITH FRACTIONAL ORDER CONTROLLERS 7. FRACTIONAL ORDER SYSTEMS Fractional derivatives provide an excellent instrument for the description of memory and hereditary properties
More informationCHAPTER 5 ROBUSTNESS ANALYSIS OF THE CONTROLLER
114 CHAPTER 5 ROBUSTNESS ANALYSIS OF THE CONTROLLER 5.1 INTRODUCTION Robust control is a branch of control theory that explicitly deals with uncertainty in its approach to controller design. It also refers
More informationA NEW APPROACH TO MIXED H 2 /H OPTIMAL PI/PID CONTROLLER DESIGN
Copyright 2002 IFAC 15th Triennial World Congress, Barcelona, Spain A NEW APPROACH TO MIXED H 2 /H OPTIMAL PI/PID CONTROLLER DESIGN Chyi Hwang,1 Chun-Yen Hsiao Department of Chemical Engineering National
More informationMULTIVARIABLE ZEROS OF STATE-SPACE SYSTEMS
Copyright F.L. Lewis All rights reserved Updated: Monday, September 9, 8 MULIVARIABLE ZEROS OF SAE-SPACE SYSEMS If a system has more than one input or output, it is called multi-input/multi-output (MIMO)
More informationPassivity-based Adaptive Inventory Control
Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference Shanghai, P.R. China, December 6-8, 29 ThB.2 Passivity-based Adaptive Inventory Control Keyu Li, Kwong Ho Chan and
More informationControl Systems II. ETH, MAVT, IDSC, Lecture 4 17/03/2017. G. Ducard
Control Systems II ETH, MAVT, IDSC, Lecture 4 17/03/2017 Lecture plan: Control Systems II, IDSC, 2017 SISO Control Design 24.02 Lecture 1 Recalls, Introductory case study 03.03 Lecture 2 Cascaded Control
More informationAPPLICATION OF ADAPTIVE CONTROLLER TO WATER HYDRAULIC SERVO CYLINDER
APPLICAION OF ADAPIVE CONROLLER O WAER HYDRAULIC SERVO CYLINDER Hidekazu AKAHASHI*, Kazuhisa IO** and Shigeru IKEO** * Division of Science and echnology, Graduate school of SOPHIA University 7- Kioicho,
More informationModel-based PID tuning for high-order processes: when to approximate
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 25 Seville, Spain, December 2-5, 25 ThB5. Model-based PID tuning for high-order processes: when to approximate
More informationUncertainty and Robustness for SISO Systems
Uncertainty and Robustness for SISO Systems ELEC 571L Robust Multivariable Control prepared by: Greg Stewart Outline Nature of uncertainty (models and signals). Physical sources of model uncertainty. Mathematical
More informationProperties of Open-Loop Controllers
Properties of Open-Loop Controllers Sven Laur University of Tarty 1 Basics of Open-Loop Controller Design Two most common tasks in controller design is regulation and signal tracking. Regulating controllers
More informationStability Margin Based Design of Multivariable Controllers
Stability Margin Based Design of Multivariable Controllers Iván D. Díaz-Rodríguez Sangjin Han Shankar P. Bhattacharyya Dept. of Electrical and Computer Engineering Texas A&M University College Station,
More informationFeedback Control of Linear SISO systems. Process Dynamics and Control
Feedback Control of Linear SISO systems Process Dynamics and Control 1 Open-Loop Process The study of dynamics was limited to open-loop systems Observe process behavior as a result of specific input signals
More informationRobust fixed-order H Controller Design for Spectral Models by Convex Optimization
Robust fixed-order H Controller Design for Spectral Models by Convex Optimization Alireza Karimi, Gorka Galdos and Roland Longchamp Abstract A new approach for robust fixed-order H controller design by
More informationEECE 460 : Control System Design
EECE 460 : Control System Design SISO Pole Placement Guy A. Dumont UBC EECE January 2011 Guy A. Dumont (UBC EECE) EECE 460: Pole Placement January 2011 1 / 29 Contents 1 Preview 2 Polynomial Pole Placement
More informationCommon Knowledge and Sequential Team Problems
Common Knowledge and Sequential Team Problems Authors: Ashutosh Nayyar and Demosthenis Teneketzis Computer Engineering Technical Report Number CENG-2018-02 Ming Hsieh Department of Electrical Engineering
More informationStability Analysis of Linear Systems with Time-varying State and Measurement Delays
Proceeding of the th World Congress on Intelligent Control and Automation Shenyang, China, June 29 - July 4 24 Stability Analysis of Linear Systems with ime-varying State and Measurement Delays Liang Lu
More informationIan G. Horn, Jeffery R. Arulandu, Christopher J. Gombas, Jeremy G. VanAntwerp, and Richard D. Braatz*
Ind. Eng. Chem. Res. 996, 35, 3437-344 3437 PROCESS DESIGN AND CONTROL Improved Filter Design in Internal Model Control Ian G. Horn, Jeffery R. Arulandu, Christopher J. Gombas, Jeremy G. VanAntwerp, and
More informationControl Systems I. Lecture 7: Feedback and the Root Locus method. Readings: Jacopo Tani. Institute for Dynamic Systems and Control D-MAVT ETH Zürich
Control Systems I Lecture 7: Feedback and the Root Locus method Readings: Jacopo Tani Institute for Dynamic Systems and Control D-MAVT ETH Zürich November 2, 2018 J. Tani, E. Frazzoli (ETH) Lecture 7:
More informationCM 3310 Process Control, Spring Lecture 21
CM 331 Process Control, Spring 217 Instructor: Dr. om Co Lecture 21 (Back to Process Control opics ) General Control Configurations and Schemes. a) Basic Single-Input/Single-Output (SISO) Feedback Figure
More informationPass Balancing Switching Control of a Four-passes Furnace System
Pass Balancing Switching Control of a Four-passes Furnace System Xingxuan Wang Department of Electronic Engineering, Fudan University, Shanghai 004, P. R. China (el: 86 656496; e-mail: wxx07@fudan.edu.cn)
More informationL 1 Adaptive Output Feedback Controller to Systems of Unknown
Proceedings of the 27 American Control Conference Marriott Marquis Hotel at Times Square New York City, USA, July 11-13, 27 WeB1.1 L 1 Adaptive Output Feedback Controller to Systems of Unknown Dimension
More information4.1 Fourier Transforms and the Parseval Identity
Chapter 4 ransfer Function Models his chapter introduces models of linear time invariant (LI) systems defined by their transfer functions(or, in general, transfer matrices). he subject is expected to be
More informationOptimal Polynomial Control for Discrete-Time Systems
1 Optimal Polynomial Control for Discrete-Time Systems Prof Guy Beale Electrical and Computer Engineering Department George Mason University Fairfax, Virginia Correspondence concerning this paper should
More informationA New Generation of Adaptive Model Based Predictive Controllers Applied in Batch Reactor Temperature Control
A New Generation of Adaptive Model Based Predictive Controllers Applied in Batch Reactor emperature Control Mihai Huzmezan University of British Columbia Pulp and Paper Centre 385 East Mall Vancouver,
More informationMCE/EEC 647/747: Robot Dynamics and Control. Lecture 12: Multivariable Control of Robotic Manipulators Part II
MCE/EEC 647/747: Robot Dynamics and Control Lecture 12: Multivariable Control of Robotic Manipulators Part II Reading: SHV Ch.8 Mechanical Engineering Hanz Richter, PhD MCE647 p.1/14 Robust vs. Adaptive
More informationAutonomous Mobile Robot Design
Autonomous Mobile Robot Design Topic: Guidance and Control Introduction and PID Loops Dr. Kostas Alexis (CSE) Autonomous Robot Challenges How do I control where to go? Autonomous Mobile Robot Design Topic:
More informationKrylov Techniques for Model Reduction of Second-Order Systems
Krylov Techniques for Model Reduction of Second-Order Systems A Vandendorpe and P Van Dooren February 4, 2004 Abstract The purpose of this paper is to present a Krylov technique for model reduction of
More informationAnalysis of SISO Control Loops
Chapter 5 Analysis of SISO Control Loops Topics to be covered For a given controller and plant connected in feedback we ask and answer the following questions: Is the loop stable? What are the sensitivities
More informationInput-output Controllability Analysis
Input-output Controllability Analysis Idea: Find out how well the process can be controlled - without having to design a specific controller Note: Some processes are impossible to control Reference: S.
More informationChapter 2. Classical Control System Design. Dutch Institute of Systems and Control
Chapter 2 Classical Control System Design Overview Ch. 2. 2. Classical control system design Introduction Introduction Steady-state Steady-state errors errors Type Type k k systems systems Integral Integral
More informationRobust QFT-based PI controller for a feedforward control scheme
Integral-Derivative Control, Ghent, Belgium, May 9-11, 218 ThAT4.4 Robust QFT-based PI controller for a feedforward control scheme Ángeles Hoyo José Carlos Moreno José Luis Guzmán Tore Hägglund Dep. of
More informationVolumes of Arithmetic Okounkov Bodies
Volumes of Arithmetic Okounkov Bodies Xinyi Yuan April 27, 2015 Contents 1 Introduction 1 2 Lattice points in a filtration 3 3 The arithmetic Okounkov body 7 1 Introduction This paper is an improvement
More informationDecoupled Feedforward Control for an Air-Conditioning and Refrigeration System
American Control Conference Marriott Waterfront, Baltimore, MD, USA June 3-July, FrB1.4 Decoupled Feedforward Control for an Air-Conditioning and Refrigeration System Neera Jain, Member, IEEE, Richard
More informationCOMPLETELY INVARIANT JULIA SETS OF POLYNOMIAL SEMIGROUPS
Series Logo Volume 00, Number 00, Xxxx 19xx COMPLETELY INVARIANT JULIA SETS OF POLYNOMIAL SEMIGROUPS RICH STANKEWITZ Abstract. Let G be a semigroup of rational functions of degree at least two, under composition
More informationParameter Estimation of Single and Decentralized Control Systems Using Pulse Response Data
Parameter Estimation of Single and Decentralized Control Systems Bull. Korean Chem. Soc. 003, Vol. 4, No. 3 79 Parameter Estimation of Single and Decentralized Control Systems Using Pulse Response Data
More informationRobust PID and Fractional PI Controllers Tuning for General Plant Model
2 مجلة البصرة للعلوم الهندسية-المجلد 5 العدد 25 Robust PID and Fractional PI Controllers Tuning for General Plant Model Dr. Basil H. Jasim. Department of electrical Engineering University of Basrah College
More informationChapter 13 Digital Control
Chapter 13 Digital Control Chapter 12 was concerned with building models for systems acting under digital control. We next turn to the question of control itself. Topics to be covered include: why one
More informationNetwork Reconstruction from Intrinsic Noise: Non-Minimum-Phase Systems
Preprints of the 19th World Congress he International Federation of Automatic Control Network Reconstruction from Intrinsic Noise: Non-Minimum-Phase Systems David Hayden, Ye Yuan Jorge Goncalves Department
More informationProblem Set 5 Solutions 1
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.245: MULTIVARIABLE CONTROL SYSTEMS by A. Megretski Problem Set 5 Solutions The problem set deals with Hankel
More informationLecture 12. Upcoming labs: Final Exam on 12/21/2015 (Monday)10:30-12:30
289 Upcoming labs: Lecture 12 Lab 20: Internal model control (finish up) Lab 22: Force or Torque control experiments [Integrative] (2-3 sessions) Final Exam on 12/21/2015 (Monday)10:30-12:30 Today: Recap
More informationRoot Locus. Signals and Systems: 3C1 Control Systems Handout 3 Dr. David Corrigan Electronic and Electrical Engineering
Root Locus Signals and Systems: 3C1 Control Systems Handout 3 Dr. David Corrigan Electronic and Electrical Engineering corrigad@tcd.ie Recall, the example of the PI controller car cruise control system.
More informationAlgorithm for Multiple Model Adaptive Control Based on Input-Output Plant Model
BULGARIAN ACADEMY OF SCIENCES CYBERNEICS AND INFORMAION ECHNOLOGIES Volume No Sofia Algorithm for Multiple Model Adaptive Control Based on Input-Output Plant Model sonyo Slavov Department of Automatics
More informationAppendix I Discrete-Data Control Systems
Appendix I Discrete-Data Control Systems O ACCOMPANY AUOMAIC CONROL SYSEMS EIGHH EDIION BY BENJAMIN C. KUO FARID GOLNARAGHI JOHN WILEY & SONS, INC. Copyright 2003 John Wiley & Sons, Inc. All rights reserved.
More informationDiscretization of Continuous Linear Anisochronic Models
Discretization of Continuous Linear Anisochronic Models Milan Hofreiter Czech echnical University in Prague Faculty of Mechanical Engineering echnicka 4, 66 7 Prague 6 CZECH REPUBLIC E-mail: hofreite@fsid.cvut.cz
More informationOptimal triangular approximation for linear stable multivariable systems
Proceedings of the 007 American Control Conference Marriott Marquis Hotel at Times Square New York City, USA, July -3, 007 Optimal triangular approximation for linear stable multivariable systems Diego
More informationEE5900 Spring Lecture 5 IC interconnect model order reduction Zhuo Feng
EE59 Spring Parallel VLSI CAD Algorithms Lecture 5 IC interconnect model order reduction Zhuo Feng 5. Z. Feng MU EE59 In theory we can apply moment matching for any order of approximation But in practice
More informationTask 1 (24%): PID-control, the SIMC method
Final Exam Course SCE1106 Control theory with implementation (theory part) Wednesday December 18, 2014 kl. 9.00-12.00 SKIP THIS PAGE AND REPLACE WITH STANDARD EXAM FRONT PAGE IN WORD FILE December 16,
More informationH 2 optimal model reduction - Wilson s conditions for the cross-gramian
H 2 optimal model reduction - Wilson s conditions for the cross-gramian Ha Binh Minh a, Carles Batlle b a School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Dai
More informationCompensatorTuning for Didturbance Rejection Associated with Delayed Double Integrating Processes, Part II: Feedback Lag-lead First-order Compensator
CompensatorTuning for Didturbance Rejection Associated with Delayed Double Integrating Processes, Part II: Feedback Lag-lead First-order Compensator Galal Ali Hassaan Department of Mechanical Design &
More informationRobust Control 9 Design Summary & Examples
Robust Control 9 Design Summary & Examples Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University 5/6/003 Outline he H Problem Solution via γ-iteration Robust stability via
More informationState-norm estimators for switched nonlinear systems under average dwell-time
49th IEEE Conference on Decision and Control December 15-17, 2010 Hilton Atlanta Hotel, Atlanta, GA, USA State-norm estimators for switched nonlinear systems under average dwell-time Matthias A. Müller
More informationHANKEL-NORM BASED INTERACTION MEASURE FOR INPUT-OUTPUT PAIRING
Copyright 2002 IFAC 15th Triennial World Congress, Barcelona, Spain HANKEL-NORM BASED INTERACTION MEASURE FOR INPUT-OUTPUT PAIRING Björn Wittenmark Department of Automatic Control Lund Institute of Technology
More informationRobust Control of Time-delay Systems
Robust Control of Time-delay Systems Qing-Chang Zhong Distinguished Lecturer, IEEE Power Electronics Society Max McGraw Endowed Chair Professor in Energy and Power Engineering Dept. of Electrical and Computer
More informationIntroduction and Preliminaries
Chapter 1 Introduction and Preliminaries This chapter serves two purposes. The first purpose is to prepare the readers for the more systematic development in later chapters of methods of real analysis
More informationOn the discrete boundary value problem for anisotropic equation
On the discrete boundary value problem for anisotropic equation Marek Galewski, Szymon G l ab August 4, 0 Abstract In this paper we consider the discrete anisotropic boundary value problem using critical
More informationKalman Filters with Uncompensated Biases
Kalman Filters with Uncompensated Biases Renato Zanetti he Charles Stark Draper Laboratory, Houston, exas, 77058 Robert H. Bishop Marquette University, Milwaukee, WI 53201 I. INRODUCION An underlying assumption
More informationLecture 6 Classical Control Overview IV. Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore
Lecture 6 Classical Control Overview IV Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore Lead Lag Compensator Design Dr. Radhakant Padhi Asst.
More informationAdaptive Control Tutorial
Adaptive Control Tutorial Petros loannou University of Southern California Los Angeles, California Baris Fidan National ICT Australia & Australian National University Canberra, Australian Capital Territory,
More informationMIMO Smith Predictor: Global and Structured Robust Performance Analysis
MIMO Smith Predictor: Global and Structured Robust Performance Analysis Ricardo S. Sánchez-Peña b,, Yolanda Bolea and Vicenç Puig Sistemas Avanzados de Control Universitat Politècnica de Catalunya (UPC)
More informationCharacterizing planar polynomial vector fields with an elementary first integral
Characterizing planar polynomial vector fields with an elementary first integral Sebastian Walcher (Joint work with Jaume Llibre and Chara Pantazi) Lleida, September 2016 The topic Ultimate goal: Understand
More informationScattering at One-Dimensional-Transmission-Line Junctions
Interaction Notes Note 603 15 March 007 Scattering at One-Dimensional-ransmission-Line Junctions Carl E. Baum University of New Mexico Department of Electrical and Computer Engineering Albuquerque New
More informationPOSITIVE REALNESS OF A TRANSFER FUNCTION NEITHER IMPLIES NOR IS IMPLIED BY THE EXTERNAL POSITIVITY OF THEIR ASSOCIATE REALIZATIONS
POSITIVE REALNESS OF A TRANSFER FUNCTION NEITHER IMPLIES NOR IS IMPLIED BY THE EXTERNAL POSITIVITY OF THEIR ASSOCIATE REALIZATIONS Abstract This letter discusses the differences in-between positive realness
More informationModel Complexity of Pseudo-independent Models
Model Complexity of Pseudo-independent Models Jae-Hyuck Lee and Yang Xiang Department of Computing and Information Science University of Guelph, Guelph, Canada {jaehyuck, yxiang}@cis.uoguelph,ca Abstract
More informationModel reduction of interconnected systems
Model reduction of interconnected systems A Vandendorpe and P Van Dooren 1 Introduction Large scale linear systems are often composed of subsystems that interconnect to each other Instead of reducing the
More informationTools from Lebesgue integration
Tools from Lebesgue integration E.P. van den Ban Fall 2005 Introduction In these notes we describe some of the basic tools from the theory of Lebesgue integration. Definitions and results will be given
More informationTRACKING AND DISTURBANCE REJECTION
TRACKING AND DISTURBANCE REJECTION Sadegh Bolouki Lecture slides for ECE 515 University of Illinois, Urbana-Champaign Fall 2016 S. Bolouki (UIUC) 1 / 13 General objective: The output to track a reference
More informationRepetitive control : Power Electronics. Applications
Repetitive control : Power Electronics Applications Ramon Costa Castelló Advanced Control of Energy Systems (ACES) Instituto de Organización y Control (IOC) Universitat Politècnica de Catalunya (UPC) Barcelona,
More informationSPECTRAL PROPERTIES OF THE LAPLACIAN ON BOUNDED DOMAINS
SPECTRAL PROPERTIES OF THE LAPLACIAN ON BOUNDED DOMAINS TSOGTGEREL GANTUMUR Abstract. After establishing discrete spectra for a large class of elliptic operators, we present some fundamental spectral properties
More informationDesign and Tuning of Fractional-order PID Controllers for Time-delayed Processes
Design and Tuning of Fractional-order PID Controllers for Time-delayed Processes Emmanuel Edet Technology and Innovation Centre University of Strathclyde 99 George Street Glasgow, United Kingdom emmanuel.edet@strath.ac.uk
More informationControl Systems I. Lecture 6: Poles and Zeros. Readings: Emilio Frazzoli. Institute for Dynamic Systems and Control D-MAVT ETH Zürich
Control Systems I Lecture 6: Poles and Zeros Readings: Emilio Frazzoli Institute for Dynamic Systems and Control D-MAVT ETH Zürich October 27, 2017 E. Frazzoli (ETH) Lecture 6: Control Systems I 27/10/2017
More informationA Note on Bode Plot Asymptotes based on Transfer Function Coefficients
ICCAS5 June -5, KINTEX, Gyeonggi-Do, Korea A Note on Bode Plot Asymptotes based on Transfer Function Coefficients Young Chol Kim, Kwan Ho Lee and Young Tae Woo School of Electrical & Computer Eng., Chungbuk
More informationFinite-time hybrid synchronization of time-delay hyperchaotic Lorenz system
ISSN 1746-7659 England UK Journal of Information and Computing Science Vol. 10 No. 4 2015 pp. 265-270 Finite-time hybrid synchronization of time-delay hyperchaotic Lorenz system Haijuan Chen 1 * Rui Chen
More informationSELECTION OF VARIABLES FOR REGULATORY CONTROL USING POLE VECTORS. Kjetil Havre 1 Sigurd Skogestad 2
SELECTION OF VARIABLES FOR REGULATORY CONTROL USING POLE VECTORS Kjetil Havre 1 Sigurd Skogestad 2 Chemical Engineering, Norwegian University of Science and Technology N-734 Trondheim, Norway. Abstract:
More informationA New Internal Model Control Method for MIMO Over-Actuated Systems
Vol. 7, No., 26 A New Internal Model Control Method for MIMO Over-Actuated Systems Ahmed Dhahri University of Tuins El Manar, National Engineering School of Tunis, Laboratory of research in Automatic Control,
More informationSome of the different forms of a signal, obtained by transformations, are shown in the figure. jwt e z. jwt z e
Transform methods Some of the different forms of a signal, obtained by transformations, are shown in the figure. X(s) X(t) L - L F - F jw s s jw X(jw) X*(t) F - F X*(jw) jwt e z jwt z e X(nT) Z - Z X(z)
More informationGo back to the main index page
1 of 10 8/24/2006 11:22 AM Go back to the main index page 1. In engineering the application of fluid mechanics in designs make much of the use of empirical results from a lot of experiments. This data
More informationW 1 æw 2 G + 0 e? u K y Figure 5.1: Control of uncertain system. For MIMO systems, the normbounded uncertainty description is generalized by assuming
Chapter 5 Robust stability and the H1 norm An important application of the H1 control problem arises when studying robustness against model uncertainties. It turns out that the condition that a control
More informationSimilarity and incomplete similarity
TIFR, Mumbai, India Refresher Course in Statistical Mechanics HBCSE Mumbai, 12 November, 2013 Copyright statement Copyright for this work remains with. However, teachers are free to use them in this form
More informationData Based Design of 3Term Controllers. Data Based Design of 3 Term Controllers p. 1/10
Data Based Design of 3Term Controllers Data Based Design of 3 Term Controllers p. 1/10 Data Based Design of 3 Term Controllers p. 2/10 History Classical Control - single controller (PID, lead/lag) is designed
More informationA C 0 coarse structure for families of pseudometrics and the Higson-Roe functor
A C 0 coarse structure for families of pseudometrics and the Higson-Roe functor Jesús P. Moreno-Damas arxiv:1410.2756v1 [math.gn] 10 Oct 2014 Abstract This paper deepens into the relations between coarse
More informationNoisy Streaming PCA. Noting g t = x t x t, rearranging and dividing both sides by 2η we get
Supplementary Material A. Auxillary Lemmas Lemma A. Lemma. Shalev-Shwartz & Ben-David,. Any update of the form P t+ = Π C P t ηg t, 3 for an arbitrary sequence of matrices g, g,..., g, projection Π C onto
More informationLMI Based Model Order Reduction Considering the Minimum Phase Characteristic of the System
LMI Based Model Order Reduction Considering the Minimum Phase Characteristic of the System Gholamreza Khademi, Haniyeh Mohammadi, and Maryam Dehghani School of Electrical and Computer Engineering Shiraz
More informationA basic canonical form of discrete-time compartmental systems
Journal s Title, Vol x, 200x, no xx, xxx - xxx A basic canonical form of discrete-time compartmental systems Rafael Bru, Rafael Cantó, Beatriz Ricarte Institut de Matemàtica Multidisciplinar Universitat
More informationWannabe-MPC for Large Systems Based on Multiple Iterative PI Controllers
Wannabe-MPC for Large Systems Based on Multiple Iterative PI Controllers Pasi Airikka, Mats Friman Metso Corp., Finland 17th Nordic Process Control Workshop Jan 26-27 2012 DTU Denmark Content Motivation
More information1.1.1 Algebraic Operations
1.1.1 Algebraic Operations We need to learn how our basic algebraic operations interact. When confronted with many operations, we follow the order of operations: Parentheses Exponentials Multiplication
More informationRepresentation of a general composition of Dirac structures
Representation of a general composition of Dirac structures Carles Batlle, Imma Massana and Ester Simó Abstract We provide explicit representations for the Dirac structure obtained from an arbitrary number
More informationSmith Predictor Based Autotuners for Time-delay Systems
Smith Predictor Based Autotuners for Time-dela Sstems ROMAN PROKOP, JIŘÍ KORBEL, RADEK MATUŠŮ Facult of Applied Informatics Tomas Bata Universit in Zlín Nám. TGM 5555, 76 Zlín CZECH REPUBLIC prokop@fai.utb.cz
More informationChaos Suppression in Forced Van Der Pol Oscillator
International Journal of Computer Applications (975 8887) Volume 68 No., April Chaos Suppression in Forced Van Der Pol Oscillator Mchiri Mohamed Syscom laboratory, National School of Engineering of unis
More informationDisturbance Attenuation Properties for Discrete-Time Uncertain Switched Linear Systems
Disturbance Attenuation Properties for Discrete-Time Uncertain Switched Linear Systems Hai Lin Department of Electrical Engineering University of Notre Dame Notre Dame, IN 46556, USA Panos J. Antsaklis
More informationAlternative Characterization of Ergodicity for Doubly Stochastic Chains
Alternative Characterization of Ergodicity for Doubly Stochastic Chains Behrouz Touri and Angelia Nedić Abstract In this paper we discuss the ergodicity of stochastic and doubly stochastic chains. We define
More informationModel reduction via tangential interpolation
Model reduction via tangential interpolation K. Gallivan, A. Vandendorpe and P. Van Dooren May 14, 2002 1 Introduction Although most of the theory presented in this paper holds for both continuous-time
More informationDUAL SPLIT QUATERNIONS AND SCREW MOTION IN MINKOWSKI 3-SPACE * L. KULA AND Y. YAYLI **
Iranian Journal of Science & echnology, ransaction A, Vol, No A Printed in he Islamic Republic of Iran, 6 Shiraz University DUAL SPLI UAERNIONS AND SCREW MOION IN MINKOWSKI -SPACE L KULA AND Y YAYLI Ankara
More informationModule 4: Time Response of discrete time systems Lecture Note 2
Module 4: Time Response of discree ime sysems Lecure Noe 2 1 Prooype second order sysem The sudy of a second order sysem is imporan because many higher order sysem can be approimaed by a second order model
More informationEEE 550 ADVANCED CONTROL SYSTEMS
UNIVERSITI SAINS MALAYSIA Semester I Examination Academic Session 2007/2008 October/November 2007 EEE 550 ADVANCED CONTROL SYSTEMS Time : 3 hours INSTRUCTION TO CANDIDATE: Please ensure that this examination
More informationQUANTIZED SYSTEMS AND CONTROL. Daniel Liberzon. DISC HS, June Dept. of Electrical & Computer Eng., Univ. of Illinois at Urbana-Champaign
QUANTIZED SYSTEMS AND CONTROL Daniel Liberzon Coordinated Science Laboratory and Dept. of Electrical & Computer Eng., Univ. of Illinois at Urbana-Champaign DISC HS, June 2003 HYBRID CONTROL Plant: u y
More informationSuppose that we have a real phenomenon. The phenomenon produces events (synonym: outcomes ).
p. 5/44 Modeling Suppose that we have a real phenomenon. The phenomenon produces events (synonym: outcomes ). Phenomenon Event, outcome We view a (deterministic) model for the phenomenon as a prescription
More informationShould we forget the Smith Predictor?
FrBT3. Should we forget the Smith Predictor? Chriss Grimholt Sigurd Skogestad* Abstract: The / controller is the most used controller in industry. However, for processes with large time delays, the common
More information