Appendix A MoReRT Controllers Design Demo Software


 Kristina O’Connor’
 1 years ago
 Views:
Transcription
1 Appendix A MoReRT Controllers Design Demo Software The use of the proposed ModelReference Robust Tuning (MoReRT) design methodology, described in Chap. 4, to tune a twodegreeoffreedom (2DoF) proportional integral derivative (PID) controller requires of an optimization program, as outlined in Sect In order to facilitate the implementation of the MoReRT approach, a MATLAB based software package has been developed. The provided routines just require the user to input the process information data and desired controller structure. The software will perform the required optimizations and show the closedloop responses for the obtained controller. In the following, a simple MoReRT software package implemented in MAT LAB is described. The user interface and software usage are explained by means of developing some design examples. This software can be obtained directly from the authors. A.1 Introduction Considered the general closedloop control system depicted in Fig. A.1 where the controlled process is given by y(s) = P u (s)u(s) + P d (s)d(s), (A.1) and the controller output signal by the expression u(s) = C r (s)r(s) + C y (s)y(s). (A.2) From (A.1) and (A.2) the closedloop control system output is then y(s) = C r(s)p u (s) 1 + C y (s)p u (s) r(s) + P d (s) d(s), (A.3) 1 + C y (s)p u (s) Springer International Publishing Switzerland 2016 V.M. Alfaro and R. Vilanova, ModelReference Robust Tuning of PID Controllers, Advances in Industrial Control, DOI /
2 170 Appendix A: MoReRT Controllers Design Demo Software Fig. A.1 General 2DoF closedloop control system block diagram that can be rewrite in compact form as y(s) = M yr (s)r(s) + M yd (s)d(s). (A.4) If P d (s) = P u (s) the disturbance d(s) actsasaninput disturbance d i (s), or load disturbance. In case that the disturbance input dynamics P d (s) = 1 the disturbance d(s) is an output disturbance d o (s). In general, if P d (s) = P u (s) the path from the disturbance to the controlled variable d y is different to the path from the controller output signal to the controlled variable u y. The controlled process model P u (s) captures the controlled variable dynamics to a change in the controller output signal and the model P d (s) the corresponding dynamics to a change in the process disturbance signal. These two dynamics can be very different. Therefore, (A.3) allows to analyze different alternatives or control problems. A.2 Controlled Process Models and Control Algorithm We consider here the general case of overdamped first and secondorder plus deadtime controlled process models, (F)SOPDT, and a controller with a 2DoF Standard PID control algorithm, PI(D) 2. Controlled Process Models The controlled process dynamics are given by following models: P u (s) = P d (s) = K pu e L pus (T pu s + 1)(a pu T pu s + 1), (A.5) K pd e L pds (T pd s + 1)(a pd T pd s + 1), (A.6) where their parameters are θ pu = { K pu = 0, T pu > 0, 0 a pu 1, L pu 0 } and θ pd = { K pd = 0, T pd 0, 0 a pd 1, L pd 0 }. Here the usual default parameter values for the derivative part have been taken.
3 Appendix A: MoReRT Controllers Design Demo Software 171 Gains of the controlled process models P u (s) and P d (s) can be any number different from zero. If K pu > 0 the controller Action must be set to Reverse (+). In case that K pu < 0 a Direct ( ) Action is required for the controller. Control Algorithm The 2DoF Standard PID control algorithm given by the equation or { u(t) = K p βr(t) y(t) + 1 t [r(ξ) y(ξ)]dξ + T i { u(s) = K p βr(s) y(s) + 1 [r(s) y(s)]+ T T i s 0 } d[γ r(t) y(t)], (A.7) dt } ds [γ r(s) y(s)] αt d s + 1 (A.8) is selected for the controller. Then, the controller parameters to tune are θ c = { K p > 0, T i > 0, T d 0, β 0, α= 0.1, γ= 0 }. The setpoint and feedback controllers are given by the transfer functions: ( C r (s) = K p β + 1 ) T i s C y (s) = K p ( T i s +, (A.9) ). (A.10) T d s 0.1T d s + 1 Normalized Controller Process Models and Controllers As described in Chap. 5 it is convenient to normalize the controlled process models and the controller. Then, using P u (s) parameters K pu and T pu and the transformation ŝ = T pu s, the normalized versions of A.5, A.6, A.9, and A.10 are: ˆP u (ŝ) = e τ Lpuŝ (ŝ + 1)(a pu ŝ + 1), (A.11) κ pd e ˆP Lpdŝ d (ŝ) = (τ pd ŝ + 1)(a pd τ pd ŝ + 1), (A.12) ( Ĉ r (ŝ) = κ p β + 1 ), τ i ŝ (A.13) ( Ĉ y (ŝ) = κ p ) τ i ŝ + τ d ŝ, 0.1τ d ŝ + 1 (A.14)
4 172 Appendix A: MoReRT Controllers Design Demo Software where τ Lpu κ pd. L pu =, T pu. K pd =,τ pd K pu. = T pd T pu,τ Lpd κ p. = K pu K p,τ i. = T i T pu,τ d. = L pd T pu,. = T d T pu, (A.15) are the new normalized (dimensionless) parameters. A.3 ClosedLoop Transfer Functions Targets and Cost Functionals Following the general procedure described in Chap. 4 and in Sect for the particular case when P d (s) = P u (s), the target closedloop servocontrol and regulatory control transfer functions for (A.4) are selected as: Myr t (ŝ) =. (τ c ŝ + 1) e τ Lpuŝ (τc 2ŝ2 + 2ζτ c ŝ + 1)(a pu τ c ŝ + 1), (A.16) Myd t (ŝ) =. (ŝ + 1)(a pu ŝ + 1) (κ pd /κ pu )(τ i /κ p ) ŝ e τ pdŝ (τ pd ŝ + 1)(a pd τ pd ŝ + 1) (τc 2ŝ2 + 2ζτ c ŝ + 1)(a pu τ c ŝ + 1), (A.17) where θ d = {ζ,τ c } are the design parameters. According to the pursued studies and analysis, presented in the corresponding chapters, there are recommended fixed values for ζ in order to guarantee a good compromise between the performance and control signal usage. On the other hand, τ c should be adjusted in order to provide the fastest response for the desired robustness. A.4 MoreRT Controllers Design Software Implementation As shown in Fig to implement the proposed MoReRT design procedure a minimum of five routines are required: a main program for data entry, a design function to call the optimization function and for iteration control, a cost function, and a simulation and plotting function. The MoReRT cost function optimization is done using MATLAB fminsearch function which uses the NelderMead simplex method. The control system simulation can be made directly in MATLAB or using a Simulink block diagram.
5 Appendix A: MoReRT Controllers Design Demo Software 173 Data Entry The user must provide the following information: The controlled process models P u (s) and P d (s) parameters: θ pu and θ pd, respectively. The controller initial normalized parameters: θc 0 (i.e. κ0 p = 1,τo i = 1,τd 0 = 0.25,β = 1). The design parameters θ d ={ζ,τ c }. For nearly nonoscillating responses ζ = 1 must be used. For under damped responses it is recommended to use ζ = 0.80 for the PI and ζ = 0.7 for the PID. The closedloop relative speed τ c can be a single value (i.e. τ c = 1), a set of discrete values (i.e. τ c = 0.8, 1.0, 1.05), or a sequence of values (i.e. τ c = 0.8 : 0.1 : 1.5). The simulation time control (total simulation time and the discretization (sampling) time). The simulation span must cover the time required for the target servocontrol and the regulatory control response to reach to a new steadystate operation. The discretization time selection impacts the total CPU time required for the cost function optimization process but also the numerical solution accuracy and stability. Cost Function The cost function evaluation include following steps: Regulatory control M yd (s) step response, yyd m (t). Regulatory control target Myd t (s) step response, yt yd (t). Regulatory control cost functional, J d = [yyd m (t) yt yd (t)]2 dt. Servocontrol M yr (s) step response, yyr m (t). Servocontrol target Myr t (s) step response, yt yr (t). Servocontrol cost functional, J r = [yyr m (t) yt yr (t)]2 dt. Total cost functional evaluation, J T = J d + J r. Controller Parameters For each τ c given, the optimization routine prints the obtained controller normalized parameters ˆθ c. With these, the corresponding control system robustness M S is evaluated. For the last design parameter τ c analyzed, the controller MoReRT tuning parameters (not the normalized ones) K P = κ p /K pu, T i = τ i T pu, T d = τ d T pu, β, α = 0.1, and γ = 0 are returned. Finally, the control system responses to a Δr setpoint change followed by a Δd disturbance change are shown with its robustness plot. The MoReRT designed controller parameters {K p, T i, T d,β} are available at the MATLAB Workspace as the variables Kpo, Tio, Tdo, and bo, respectively. Demo Software Files MoReRTcPID2pSOPuPd.p: main program, data entry and program execution control.
6 174 Appendix A: MoReRT Controllers Design Demo Software Fig. A.2 Program main menu user interface mrtfpcpid2psopupd.p: design parameter τ c iteration control, optimization function call. mrtfccpid2psopupd.p: cost function evaluation. mrtfscpid2psopupd.p: control systems simulation, step responses and robustness plot. mrtfgnyquist.p: Nyquist with M S circles plot. MATLAB functions: bode, disp, fminsearch, lsim, nyquist, plot, step. Program Main Menu The MoReRT demo software user interface ([MAIN MENU]) is shown in Fig. A.2. Using the MAIN MENU push buttons the user can input the problem data (design parameters, controlled process (F)SOPDT models parameters, PI(D) controller initial parameters, and simulation control), run the controller tuning routine, and/or exit the control system design process. Input Data Error Detection The MoReRT demo software implements a simple verification of the input data provided by the user to prevent an eventual program malfunction or hanging. Some of the error messages are shown in Fig. A.3. A.5 MoReRT Controllers Design Demo Software Usage For use of the MoReRT controllers design demo software consider the following example
7 Appendix A: MoReRT Controllers Design Demo Software 175 Fig. A.3 Input data error messages Controlled process models: 2e 2.0s P u (s) = (5.0s + 1)(2.5s + 1), P d (s) = P u (s). Controller: 2DoF PI. Design criteria: MS t 1.80, ζ = 0.80, τ c = 1.0 (only one initial test). Controller initial normalized parameters: κ 0 p = 1.0, τ i 0 = 1.0, τd 0 = 0, β = 1.0. Simulation control: t u = δt = 0.02 (for simulations during optimization), t us = δt s = 0.2, Δr = 10 %, Δd = 5 % (for final control system simulation). Design for Input Disturbance For the first example, the disturbance transfer function is selected as P d (s) = P u (s). Then, we are considering an input disturbance d i (s). The Execution of the MoReRT Design Demo Software maim program is started writing the main file name at MATLAB Command Window:»MoReRTcPID2pSOPuPd [Enter] After that, the program Main Menu shown in Fig. A.2 is displayed. Data Input User must provide the control problem data. The problem data input windows are selected from the MAIN MENU: [DESIGN Parameters], opens the window shown in Fig. A.4. [CONTROLLED PROCESSES Parameters], opens the window shown in Fig. A.5.
8 176 Appendix A: MoReRT Controllers Design Demo Software Fig. A.4 Design parameters input window Fig. A.5 Controlled process P u (s) parameters input window [CONTROLLER Parameters], opens the window shown in Fig. A.6. [SIMULATION Control], opens the window shown in Fig. A.7. Program Output The program output is: == MoReRT Controllers Design (cpid2/psopdt) == ============================================== Controlled process models parameters Pu(s): Kpu = 2 Tpu = 5 apu = 0.5 Lpu = 2
9 Appendix A: MoReRT Controllers Design Demo Software 177 Fig. A.6 PI Controller initial normalized parameters input window Fig. A.7 Control system simulation control input window Pd(s) = Pu(s) Design parameters controller: PI2 z = 0.8 tco = 1 MoReRT controller normalized parameters tc = 1
10 178 Appendix A: MoReRT Controllers Design Demo Software kp = ti = td = 0 ba = Ms = == MoReRT PID2 controller parameters == Action = reverse (+) Kp = Ti = Td = 0 alpha = 0.1 beta = gamma = 0 Ms = 1.573» The robustness of the control system M S = 1.57 is higher that the design requirement. Then, we can increase the control system speed and use tcv = 0.95:0.05:0.85, to obtain three controllers. Therefore looking for a better performance on the basis of the desired robustness. Selecting from the MAIN MENU the [DESIGN Parameters] input window the new closedloop relative speed design parameters are typed as shown in Fig. A.8 Design Progress Bar During the design process its progress is indicated by a length changing red bar as showninfig.a.9. The design process can be interrupted with the [Cancel] push button. It will be stopped after that the optimization with the next τ c design parameter is finished. Fig. A.8 Change of the closedloop relative speeds
11 Appendix A: MoReRT Controllers Design Demo Software 179 Fig. A.9 Controller design progress bar New Results The program output is now: == MoReRT Controllers Design (cpid2/psopdt) == ==============================================... MoReRT controller normalized parameters tc = 0.95 kp = ti = td = 0 ba = Ms = tc = 0.9 kp = ti = td = 0 ba = Ms = tc = 0.85 kp = 1.1 ti = td = 0 ba = Ms = == MoReRT PID2 controller parameters == Action = reverse (+) Kp = 0.55 Ti = Td = 0 alpha = 0.1
12 180 Appendix A: MoReRT Controllers Design Demo Software y(t), r(t), u(t), d(t) [%] MoReRT Control System Performance y(t) r(t) u(t) d(t) L (jω) Robustness M S =1.2 M =2.0 S 1 L(jω) M = S L(jω) time, t [controlled process model time units] L (jω) Fig. A.10 Demo example (d i ) System responses and robustness (τ c = 0.85) beta = gamma = 0 Ms = » For τ c = 0.85 the control system robustness is M S = Then, we select a PI 2 controller with parameters K p = 0.55, T i = 6.49, and β = The resulting control systems responses and robustness are shown in Fig. A.10. Design for Output Disturbance To design the MoReRT controller considering an output disturbance d o the transfer function P d (s) = 1. Then, Kpd = 1, Tpd = 0, apd = 0, and Lpd = 0 are automatically set. Selecting at the [DESIGN Parameters] input window the control problem 2 (Pd = 1) and using z = 0.8 and tcv = 0.85 as shown in Fig. A.11,wehave == MoReRT Controllers Design (cpid2/psopdt) == ==============================================... MoReRT controller normalized parameters tc = 0.85 kp = ti = td = 0 ba = Ms = == MoReRT PID2 controller parameters == Action = reverse (+)
13 Appendix A: MoReRT Controllers Design Demo Software 181 Fig. A.11 Output disturbance selection Kp = Ti = Td = 0 alpha = 0.1 beta = gamma = 0 Ms = » Using the same closedloop system relative speed design parameter, the resulting control system for an output disturbance is more oscillating, with higher peak error, and less robust than the one designed by considering an input disturbance. The new control systems responses and robustness are shown in Fig. A.12. To compare, at the same design robustness level, the control system obtained considering an output disturbance with the one obtained earlier considering an input disturbance the control system relative speed must be decreased. Adjusting tc we finally obtain: == MoReRT Controllers Design (cpid2/psopdt) == ============================================== Controlled process models parameters Pu(s): Kpu = 2 Tpu = 5 apu = 0.5 Lpu = 2 Pd(s) = 1
14 182 Appendix A: MoReRT Controllers Design Demo Software y(t), r(t), u(t), d(t) [%] MoReRT Control System Performance y(t) r(t) u(t) d(t) L (jω) Robustness M S =1.2 M S =2.0 1 L(jω) M = S L(jω) time, t [controlled process model time units] L (jω) Fig. A.12 Demo example (d o ) System responses and robustness (τ c = 0.85) Design parameters controller: PI2 z = 0.8 tco = MoReRT controller normalized parameters tc = kp = ti = td = 0 ba = Ms = == MoReRT PID2 controller parameters == Action = reverse (+) Kp = Ti = Td = 0 alpha = 0.1 beta = gamma = 0 Ms = » The responses of the new controller are shown in Fig. A.13. The parameters of the two PI 2 controllers are listed in Table A.1. These two controller parameters sets are different but produce control systems with the same robustness level.
15 Appendix A: MoReRT Controllers Design Demo Software 183 y(t), r(t), u(t), d(t) [%] MoReRT Control System Performance y(t) r(t) u(t) d(t) L (jω) Robustness M S =1.2 M S =2.0 1 L(jω) M = S L(jω) time, t [controlled process model time units] L (jω) Fig. A.13 Demo example (d o ) New system responses and robustness (τ c = 0.895) Table A.1 MoReRT PI 2 parameters Disturbance τ c K p T i β M S d i d o Design for a Slow Disturbance Consider now that the main disturbance dynamics has been identified and that it is slower than early assumed and with a negative and lower gain. It is given by the model 0.5e 4.0s P d (s) = (7.5s + 1)(5.625s + 1). The robustness requirement is increased to MS t = The only data that needs to be changed is shown if Figs. A.14 ([DESIGN Parameters]) and A.15 ([CONTROLLED PROCESSES Parameters]). The program output data is:» MoReRT_cPID2pSOPuPd == MoReRT Controllers Design (cpid2/psopdt) == ============================================== Controlled process models parameters Pu(s): Kpu = 2 Tpu = 5 apu = 0.5 Lpu = 2
16 184 Appendix A: MoReRT Controllers Design Demo Software Fig. A.14 New desing parameters Fig. A.15 Controlled process data (P d (s) = Pu(s))
17 Appendix A: MoReRT Controllers Design Demo Software 185 Pd(s): Kpd = 0.5 Tpd = 7.5 apd = 0.75 Lpd = 4 Design parameters controller: PI2 z = 0.8 tco = 1 MoReRT controller normalized parameters tc = 1 kp = ti = td = 0 ba = Ms = tc = 0.9 kp = ti = td = 0 ba = Ms = tc = 0.8 kp = ti = td = 0 ba = Ms = tc = 0.75 kp = ti = td = 0 ba = Ms = == MoReRT PID2 controller parameters == Action = reverse (+) Kp = Ti = Td = 0
18 186 Appendix A: MoReRT Controllers Design Demo Software y(t), r(t), u(t), d(t) [%] MoReRT Control System Performance y(t) r(t) u(t) d(t) L (jω) Robustness M S =1.2 M =2.0 S 1 L(jω) M = S L(jω) time, t [controlled process model time units] L(jω) Fig. A.16 Demo example P d (s) = P u (s) (slow disturbance) System responses and robustness alpha = 0.1 beta = gamma = 0 Ms = » The PI 2 control system response obtained with τ c = 0.75 has the required robustness M S = Its response is shown in Fig. A.16. It is noted that in this case the controller proportional setpoint weight needs a value β>1(beta =1.145). MoReRT PID 2 Controller For comparison with the PI 2 controller PID 2 controllers are obtained using z = 0.70 and tcv = 0.65:0.05:0.75. The changes in the input data are shown in Figs. A.17 ([DESIGN Parameters]) and A.18 ([CONTROLLER Parameters]). The PID design gives: == MoReRT controllers design (cpid2/psopdt) == ==============================================... Design parameters controller: PID2 z = 0.7 tco = MoReRT controller normalized parameters tc = 0.65
19 Appendix A: MoReRT Controllers Design Demo Software 187 Fig. A.17 New design parameters for PID 2 Fig. A.18 PID controller normalized initial parameters kp = ti = td = ba = Ms = tc = 0.7 kp = ti = td = ba = Ms =
20 188 Appendix A: MoReRT Controllers Design Demo Software tc = 0.75 kp = ti = td = ba = Ms = == MoReRT PID2 controller parameters == Action = reverse (+) Kp = Ti = Td = alpha = 0.1 beta = gamma = 0 Ms = » Parameters of the PI 2 and PID 2 controllers are listed in Table A.2. For the same robustness, the PID 2 control system provides a faster disturbance recovery and with Table A.2 MoReRT PI 2 and PID 2 parameters Controller K p T i T d β M S PI PID y(t), r(t), u(t), d(t) [%] MoReRT Control System Performance y(t) r(t) u(t) d(t) L (jω) Robustness M S =1.2 M =2.0 S 1 L(jω) M = S L(jω) time, t [controlled process model time units] L (jω) Fig. A.19 Demo example PID 2 (P d (s) = P u (s)) System responses and robustness
21 Appendix A: MoReRT Controllers Design Demo Software 189 lower maximum error than the PI 2. Its setpoint response is also faster but with a higher overshoot, as seen in Fig. A.19. Select [EXIT] from the MAIN MENU to close the program and return to MAT LAB.
22 Index C Closedloop reference models, 33, 147 Commercial controllers, 7, 55, 129, 145, 165 Control algorithm, 7, 15, 16, 42 proportional integral, 7, 8, 42, 107 proportional integral derivative, 7 9, 11, 12, 15, 16, 18, 23, 39, 55, 129, 132, 169 Control effort, 1, 8, 18, 21, 23, 27, 32, 34, 52, 53, 60, 61, 64, 70, 72, 74 77, 82, 87, 89, 91, 96, 100, 101, 105, 106, 109 Controlled process integrating, 4, 79, 91, 93, 105, 141 inverse response, 4, 37, 65, 68, 70, 75, 114, 141, 142, 145, 148 overdamped, 3, 4, 37, 41, 53, 55, 60, 84, 105, 107, 109, 145 unstable, 4, 93 96, 105, 145 Controlled process models firstorder plus deadtime, 36, 37, 39 41, 47, 55, 60, 96 99, 108, 136 secondorder plus dead time, 36, 37, 40 Controlled variable, 1, 3, 7, 22, 23, 30, 33, 43, 84, 105, 106, 109, 111, 112, 114, 119, 120, 155, 165, 170 Controller parallel, 39 PI, 42, 50, 60, 62, 72, 74, 77, 79, 81, 83, 96, 119, 158 PID, 2, 3, 13, 14, 16, 32, 35, 36, 41, 55, 56, 60, 64, 74, 75, 77, 86, 96, 105, 111, 119, 126, 129, 130, 132, 137, 140, 149 standard, 39, 119, 132, 140 Control system, 2, 21 27, 29, 30, 32, 33, 42, 52, 59, 75, 80, 93, 94, 96, , 108, 115, 117, 118, 125, 126, 147, 148, 156, 178, 188 Cost functionals, 31, 108, 172 D Deadtime compensating, 119, 120, 125, 126 Disturbance, 1, 7, 23, 30, 51, 70, 88, 89, 105, 109, 111, 112, , 120, 122, 126, 130, 146, 147, 159, 163, 170, 173, 175, 181 E Evaluation metrics control effort, 21, 23 fragility, 21, 24 performance, 2, 3, 41, 70 robustness, 21, 23, 173 F Fragility, 3, 21, M Maximum sensitivity, 3, 24, 25, 32, 56, 105, 108, 122, 125 Modelreference, 4, 31, 32, 34, 59, 62 N Normalized controlled process model, 40, 129 Normalized controller, 36, 38, 39, 66, 82, 171 P Performance indices, 49, 62, 75, 100, 158 Springer International Publishing Switzerland 2016 V.M. Alfaro and R. Vilanova, ModelReference Robust Tuning of PID Controllers, Advances in Industrial Control, DOI /
23 192 Index R Regulatory control, 3, 7, 26, 30, 31, 33, 34, 42, 43, 49 51, 58, 60, 70, 71, 75, 76, 86, 87, 90, 112, 148, 172 Robustness, 3, 18, 23 25, 27, 32, 43, 44, 49, 50, 60, 61, 66, 70, 72, 75, 76, 81, 85, 87, 89, 96, 99, 102, 105, 108, 109, 111, 117, 121, 122, 126, 132, 141, 146, 148, 158, 163, 165 S Servocontrol, 3, 7, 16, 26, 30, 32, 34, 42, 43, 51, 52, 54, 59, 62, 75, 86, 89, 93, 105, 112, 121, 122, 125, 140, 165, 172, 173 Setpoint, 1, 3, 7, 10, 18, 21 23, 30, 33, 34, 48, 59, 60, 70, 86, 89, 101, 102, 105, 108, 111, , 135, 140, 159, 165, 186 Stirredtank heater, 149, 165 T Tuning rule, 2, 3, 7, 12, 23, 25, 27, 35, 40, 81, 97, 101, 129, 140, 141, 148, 165 Twodegreeoffreedom, 2, 3, 9, 30, 43, 116, 129, 130, , 137, 139, 140, 165
CHAPTER 10: STABILITY &TUNING
When I complete this chapter, I want to be able to do the following. Determine the stability of a process without control Determine the stability of a closedloop feedback control system Use these approaches
More informationAutomatic Control 2. Loop shaping. Prof. Alberto Bemporad. University of Trento. Academic year
Automatic Control 2 Loop shaping Prof. Alberto Bemporad University of Trento Academic year 21211 Prof. Alberto Bemporad (University of Trento) Automatic Control 2 Academic year 21211 1 / 39 Feedback
More informationRaktim Bhattacharya. . AERO 422: Active Controls for Aerospace Vehicles. Basic Feedback Analysis & Design
AERO 422: Active Controls for Aerospace Vehicles Basic Feedback Analysis & Design Raktim Bhattacharya Laboratory For Uncertainty Quantification Aerospace Engineering, Texas A&M University Routh s Stability
More informationPart II. Advanced PID Design Methods
Part II Advanced PID Design Methods 54 Controller transfer function C(s) = k p (1 + 1 T i s + T d s) (71) Many extensions known to the basic design methods introduced in RT I. Four advanced approaches
More informationFeedback Control of Linear SISO systems. Process Dynamics and Control
Feedback Control of Linear SISO systems Process Dynamics and Control 1 OpenLoop Process The study of dynamics was limited to openloop systems Observe process behavior as a result of specific input signals
More informationEE3CL4: Introduction to Linear Control Systems
1 / 17 EE3CL4: Introduction to Linear Control Systems Section 7: McMaster University Winter 2018 2 / 17 Outline 1 4 / 17 Cascade compensation Throughout this lecture we consider the case of H(s) = 1. We
More informationarxiv: v1 [cs.sy] 30 Nov 2017
Disturbance Observer based Control of Integrating Processes with DeadTime using PD controller Sujay D. Kadam SysIDEA Lab, IIT Gandhinagar, India. arxiv:1711.11250v1 [cs.sy] 30 Nov 2017 Abstract The work
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 Steadystate Steadystate errors errors Type Type k k systems systems Integral Integral
More informationYTÜ Mechanical Engineering Department
YTÜ Mechanical Engineering Department Lecture of Special Laboratory of Machine Theory, System Dynamics and Control Division Coupled Tank 1 Level Control with using Feedforward PI Controller Lab Date: Lab
More informationAN INTRODUCTION TO THE CONTROL THEORY
OpenLoop controller An OpenLoop (OL) controller is characterized by no direct connection between the output of the system and its input; therefore external disturbance, nonlinear dynamics and parameter
More informationTask 1 (24%): PIDcontrol, the SIMC method
Final Exam Course SCE1106 Control theory with implementation (theory part) Wednesday December 18, 2014 kl. 9.0012.00 SKIP THIS PAGE AND REPLACE WITH STANDARD EXAM FRONT PAGE IN WORD FILE December 16,
More informationLecture 12. Upcoming labs: Final Exam on 12/21/2015 (Monday)10:3012:30
289 Upcoming labs: Lecture 12 Lab 20: Internal model control (finish up) Lab 22: Force or Torque control experiments [Integrative] (23 sessions) Final Exam on 12/21/2015 (Monday)10:3012:30 Today: Recap
More informationCHAPTER 3 TUNING METHODS OF CONTROLLER
57 CHAPTER 3 TUNING METHODS OF CONTROLLER 3.1 INTRODUCTION This chapter deals with a simple method of designing PI and PID controllers for first order plus time delay with integrator systems (FOPTDI).
More informationDouble Inverted Pendulum (DBIP)
Linear Motion Servo Plant: IP01_2 Linear Experiment #15: LQR Control Double Inverted Pendulum (DBIP) All of Quanser s systems have an inherent open architecture design. It should be noted that the following
More informationCYBER EXPLORATION LABORATORY EXPERIMENTS
CYBER EXPLORATION LABORATORY EXPERIMENTS 1 2 Cyber Exploration oratory Experiments Chapter 2 Experiment 1 Objectives To learn to use MATLAB to: (1) generate polynomial, (2) manipulate polynomials, (3)
More informationCHAPTER 13: FEEDBACK PERFORMANCE
When I complete this chapter, I want to be able to do the following. Apply two methods for evaluating control performance: simulation and frequency response Apply general guidelines for the effect of 
More informationDesign and Tuning of Fractionalorder PID Controllers for Timedelayed Processes
Design and Tuning of Fractionalorder PID Controllers for Timedelayed Processes Emmanuel Edet Technology and Innovation Centre University of Strathclyde 99 George Street Glasgow, United Kingdom emmanuel.edet@strath.ac.uk
More informationAnalysis and Design of Control Systems in the Time Domain
Chapter 6 Analysis and Design of Control Systems in the Time Domain 6. Concepts of feedback control Given a system, we can classify it as an open loop or a closed loop depends on the usage of the feedback.
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.04A Systems and Controls Spring 2013
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.04A Systems and Controls Spring 2013 Problem Set #4 Posted: Thursday, Mar. 7, 13 Due: Thursday, Mar. 14, 13 1. Sketch the Root
More informationControl of Manufacturing Processes
Control of Manufacturing Processes Subject 2.830 Spring 2004 Lecture #18 Basic Control Loop Analysis" April 15, 2004 Revisit Temperature Control Problem τ dy dt + y = u τ = time constant = gain y ss =
More informationRoot Locus. Motivation Sketching Root Locus Examples. School of Mechanical Engineering Purdue University. ME375 Root Locus  1
Root Locus Motivation Sketching Root Locus Examples ME375 Root Locus  1 Servo Table Example DC Motor Position Control The block diagram for position control of the servo table is given by: D 0.09 Position
More informationProcess Control J.P. CORRIOU. Reaction and Process Engineering Laboratory University of LorraineCNRS, Nancy (France) Zhejiang University 2016
Process Control J.P. CORRIOU Reaction and Process Engineering Laboratory University of LorraineCNRS, Nancy (France) Zhejiang University 206 J.P. Corriou (LRGP) Process Control Zhejiang University 206
More informationExperiment 81  Design of a Feedback Control System
Experiment 81  Design of a Feedback Control System 201139030 (Group 44) ELEC273 May 9, 2016 Abstract This report discussed the establishment of openloop system using FOPDT medel which is usually used
More informationControl Systems I Lecture 10: System Specifications
Control Systems I Lecture 10: System Specifications Readings: Guzzella, Chapter 10 Emilio Frazzoli Institute for Dynamic Systems and Control DMAVT ETH Zürich November 24, 2017 E. Frazzoli (ETH) Lecture
More informationIntroduction to Feedback Control
Introduction to Feedback Control Control System Design Why Control? OpenLoop vs ClosedLoop (Feedback) Why Use Feedback Control? ClosedLoop Control System Structure Elements of a Feedback Control System
More information1 Loop Control. 1.1 Openloop. ISS0065 Control Instrumentation
Lecture 4 ISS0065 Control Instrumentation 1 Loop Control System has a continuous signal (analog) basic notions: openloop control, closeloop control. 1.1 Openloop Openloop / avatud süsteem / открытая
More informationDynamic Behavior. Chapter 5
1 Dynamic Behavior In analyzing process dynamic and process control systems, it is important to know how the process responds to changes in the process inputs. A number of standard types of input changes
More informationBangladesh University of Engineering and Technology. EEE 402: Control System I Laboratory
Bangladesh University of Engineering and Technology Electrical and Electronic Engineering Department EEE 402: Control System I Laboratory Experiment No. 4 a) Effect of input waveform, loop gain, and system
More informationClassify a transfer function to see which order or ramp it can follow and with which expected error.
Dr. J. Tani, Prof. Dr. E. Frazzoli 505900 Control Systems I (Autumn 208) Exercise Set 0 Topic: Specifications for Feedback Systems Discussion: 30.. 208 Learning objectives: The student can grizzi@ethz.ch,
More informationIterative Controller Tuning Using Bode s Integrals
Iterative Controller Tuning Using Bode s Integrals A. Karimi, D. Garcia and R. Longchamp Laboratoire d automatique, École Polytechnique Fédérale de Lausanne (EPFL), 05 Lausanne, Switzerland. email: alireza.karimi@epfl.ch
More informationAnswers to multiple choice questions
Answers to multiple choice questions Chapter 2 M2.1 (b) M2.2 (a) M2.3 (d) M2.4 (b) M2.5 (a) M2.6 (b) M2.7 (b) M2.8 (c) M2.9 (a) M2.10 (b) Chapter 3 M3.1 (b) M3.2 (d) M3.3 (d) M3.4 (d) M3.5 (c) M3.6 (c)
More informationClosed Loop Identification Of A First Order Plus Dead Time Process Model Under PI Control
Dublin Institute of Technology RROW@DIT Conference papers School of Electrical and Electronic Engineering 6 Closed Loop Identification Of First Order Plus Dead Time Process Model Under PI Control Tony
More informationMultivariable Control Laboratory experiment 2 The Quadruple Tank 1
Multivariable Control Laboratory experiment 2 The Quadruple Tank 1 Department of Automatic Control Lund Institute of Technology 1. Introduction The aim of this laboratory exercise is to study some different
More informationAppendix A Prototypes Models
Appendix A Prototypes Models This appendix describes the model of the prototypes used in Chap. 3. These mathematical models can also be found in the Student Handout by Quanser. A.1 The QUANSER SRV02 Setup
More informationIMC 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 informationModel based control design
Model based control design Alf Isaksson September, 999 Supplied as supplement to course book in Automatic Control Basic course (Reglerteknik AK) Objective: To introduce some general approaches to model
More informationProfessor Fearing EE C128 / ME C134 Problem Set 7 Solution Fall 2010 Jansen Sheng and Wenjie Chen, UC Berkeley
Professor Fearing EE C8 / ME C34 Problem Set 7 Solution Fall Jansen Sheng and Wenjie Chen, UC Berkeley. 35 pts Lag compensation. For open loop plant Gs ss+5s+8 a Find compensator gain Ds k such that the
More informationLinear State Feedback Controller Design
Assignment For EE5101  Linear Systems Sem I AY2010/2011 Linear State Feedback Controller Design Phang Swee King A0033585A Email: king@nus.edu.sg NGS/ECE Dept. Faculty of Engineering National University
More informationDepartment of Electrical and Computer Engineering. EE461: Digital Control  Lab Manual
Department of Electrical and Computer Engineering EE461: Digital Control  Lab Manual Winter 2011 EE 461 Experiment #1 Digital Control of DC Servomotor 1 Objectives The objective of this lab is to introduce
More informationA Tuning of the Nonlinear PI Controller and Its Experimental Application
Korean J. Chem. Eng., 18(4), 451455 (2001) A Tuning of the Nonlinear PI Controller and Its Experimental Application Doe Gyoon Koo*, Jietae Lee*, Dong Kwon Lee**, Chonghun Han**, Lyu Sung Gyu, Jae Hak
More informationPosition Control Experiment MAE171a
Position Control Experiment MAE171a January 11, 014 Prof. R.A. de Callafon, Dept. of MAE, UCSD TAs: Jeff Narkis, email: jnarkis@ucsd.edu Gil Collins, email: gwcollin@ucsd.edu Contents 1 Aim and Procedure
More informationLaboratory 11 Control Systems Laboratory ECE3557. State Feedback Controller for Position Control of a Flexible Joint
Laboratory 11 State Feedback Controller for Position Control of a Flexible Joint 11.1 Objective The objective of this laboratory is to design a full state feedback controller for endpoint position control
More informationAppendix A: Exercise Problems on Classical Feedback Control Theory (Chaps. 1 and 2)
Appendix A: Exercise Problems on Classical Feedback Control Theory (Chaps. 1 and 2) For all calculations in this book, you can use the MathCad software or any other mathematical software that you are familiar
More informationHandson Lab. Damped Compound Pendulum System ID (Experimental and Simulation) L Bar length m d Pivot to CG distance m m Mass of pendulum kg
Handson Lab Damped Compound Pendulum System ID (Experimental and Simulation) Preamble: c d dt d L Bar length m d Pivot to CG distance m m Mass of pendulum kg L L m g L Sketched above is a damped compound
More informationDr Ian R. Manchester
Week Content Notes 1 Introduction 2 Frequency Domain Modelling 3 Transient Performance and the splane 4 Block Diagrams 5 Feedback System Characteristics Assign 1 Due 6 Root Locus 7 Root Locus 2 Assign
More informationVALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING SUBJECT QUESTION BANK : EC6405 CONTROL SYSTEM ENGINEERING SEM / YEAR: IV / II year
More informationLecture 14  Using the MATLAB Control System Toolbox and Simulink Friday, February 8, 2013
Today s Objectives ENGR 105: Feedback Control Design Winter 2013 Lecture 14  Using the MATLAB Control System Toolbox and Simulink Friday, February 8, 2013 1. introduce the MATLAB Control System Toolbox
More informationINTERACTIVE APPLICATIONS IN A MANDATORY CONTROL COURSE
INTERACTIVE APPLICATIONS IN A MANDATORY CONTROL COURSE Yves Piguet Roland Longchamp Calerga Sàrl, av. de la Chablière 35, 4 Lausanne, Switzerland. Email: yves.piguet@calerga.com Laboratoire d automatique,
More informationVALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur 603 203. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING SUBJECT QUESTION BANK : EC6405 CONTROL SYSTEM ENGINEERING SEM / YEAR: IV / II year
More informationRotary Motion Servo Plant: SRV02. Rotary Experiment #11: 1DOF Torsion. 1DOF Torsion Position Control using QuaRC. Student Manual
Rotary Motion Servo Plant: SRV02 Rotary Experiment #11: 1DOF Torsion 1DOF Torsion Position Control using QuaRC Student Manual Table of Contents 1. INTRODUCTION...1 2. PREREQUISITES...1 3. OVERVIEW OF
More informationState space control for the Two degrees of freedom Helicopter
State space control for the Two degrees of freedom Helicopter AAE364L In this Lab we will use state space methods to design a controller to fly the two degrees of freedom helicopter. 1 The state space
More information6.1 Sketch the zdomain root locus and find the critical gain for the following systems K., the closedloop characteristic equation is K + z 0.
6. Sketch the zdomain root locus and find the critical gain for the following systems K (i) Gz () z 4. (ii) Gz K () ( z+ 9. )( z 9. ) (iii) Gz () Kz ( z. )( z ) (iv) Gz () Kz ( + 9. ) ( z. )( z 8. ) (i)
More informationControls Problems for Qualifying Exam  Spring 2014
Controls Problems for Qualifying Exam  Spring 2014 Problem 1 Consider the system block diagram given in Figure 1. Find the overall transfer function T(s) = C(s)/R(s). Note that this transfer function
More informationCascade Control of a Continuous Stirred Tank Reactor (CSTR)
Journal of Applied and Industrial Sciences, 213, 1 (4): 1623, ISSN: 23284595 (PRINT), ISSN: 2328469 (ONLINE) Research Article Cascade Control of a Continuous Stirred Tank Reactor (CSTR) 16 A. O. Ahmed
More informationPD, PI, PID Compensation. M. Sami Fadali Professor of Electrical Engineering University of Nevada
PD, PI, PID Compensation M. Sami Fadali Professor of Electrical Engineering University of Nevada 1 Outline PD compensation. PI compensation. PID compensation. 2 PD Control L= loop gain s cl = desired closedloop
More informationPID Control. Objectives
PID Control Objectives The objective of this lab is to study basic design issues for proportionalintegralderivative control laws. Emphasis is placed on transient responses and steadystate errors. The
More informationSRV02Series Rotary Experiment # 1. Position Control. Student Handout
SRV02Series Rotary Experiment # 1 Position Control Student Handout SRV02Series Rotary Experiment # 1 Position Control Student Handout 1. Objectives The objective in this experiment is to introduce the
More informationDCmotor PID control
DCmotor PID control This version: March 2, 2018 REGLERTEKNIK Name: Pnumber: AUTOMATIC LINKÖPING CONTROL Date: Passed: Chapter 1 Introduction The purpose of this lab is to give an introduction to PID
More informationDCmotor PID control
DCmotor PID control This version: November 1, 2017 REGLERTEKNIK Name: Pnumber: AUTOMATIC LINKÖPING CONTROL Date: Passed: Chapter 1 Introduction The purpose of this lab is to give an introduction to
More informationAircraft Stability & Control
Aircraft Stability & Control Textbook Automatic control of Aircraft and missiles 2 nd Edition by John H Blakelock References Aircraft Dynamics and Automatic Control  McRuler & Ashkenas Aerodynamics, Aeronautics
More informationINTRODUCTION TO DIGITAL CONTROL
ECE4540/5540: Digital Control Systems INTRODUCTION TO DIGITAL CONTROL.: Introduction In ECE450/ECE550 Feedback Control Systems, welearnedhow to make an analog controller D(s) to control a lineartimeinvariant
More informationIterative Feedback Tuning
Iterative Feedback Tuning Michel Gevers CESAME  UCL LouvainlaNeuve Belgium Collaboration : H. Hjalmarsson, S. Gunnarsson, O. Lequin, E. Bosmans, L. Triest, M. Mossberg Outline Problem formulation Iterative
More informationMassachusetts Institute of Technology Department of Mechanical Engineering Dynamics and Control II Design Project
Massachusetts Institute of Technology Department of Mechanical Engineering.4 Dynamics and Control II Design Project ACTIVE DAMPING OF TALL BUILDING VIBRATIONS: CONTINUED Franz Hover, 5 November 7 Review
More informationPID controllers, part I
Faculty of Mechanical and Power Engineering Dr inŝ. JANUSZ LICHOTA CONTROL SYSTEMS PID controllers, part I Wrocław 2007 CONTENTS Controller s classification PID controller what is it? Typical controller
More informationSolutions for Tutorial 10 Stability Analysis
Solutions for Tutorial 1 Stability Analysis 1.1 In this question, you will analyze the series of three isothermal CSTR s show in Figure 1.1. The model for each reactor is the same at presented in Textbook
More informationSubject: Introduction to Process Control. Week 01, Lectures 01 02, Spring Content
v CHEG 461 : Process Dynamics and Control Subject: Introduction to Process Control Week 01, Lectures 01 02, Spring 2014 Dr. Costas Kiparissides Content 1. Introduction to Process Dynamics and Control 2.
More informationPole placement control: state space and polynomial approaches Lecture 2
: state space and polynomial approaches Lecture 2 : a state O. Sename 1 1 Gipsalab, CNRSINPG, FRANCE Olivier.Sename@gipsalab.fr www.gipsalab.fr/ o.sename based November 21, 2017 Outline : a state
More informationThe loop shaping paradigm. Lecture 7. Loop analysis of feedback systems (2) Essential specifications (2)
Lecture 7. Loop analysis of feedback systems (2). Loop shaping 2. Performance limitations The loop shaping paradigm. Estimate performance and robustness of the feedback system from the loop transfer L(jω)
More informationLoworder feedbackfeedforward controller for deadtime processes with measurable disturbances
Preprint, 11th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems Loworder feedbackfeedforward controller for deadtime processes with measurable disturbances Carlos Rodríguez
More informationProfessional Portfolio Selection Techniques: From Markowitz to Innovative Engineering
Massachusetts Institute of Technology Sponsor: Electrical Engineering and Computer Science Cosponsor: Science Engineering and Business Club Professional Portfolio Selection Techniques: From Markowitz to
More informationChapter 8. Feedback Controllers. Figure 8.1 Schematic diagram for a stirredtank blending system.
Feedback Controllers Figure 8.1 Schematic diagram for a stirredtank blending system. 1 Basic Control Modes Next we consider the three basic control modes starting with the simplest mode, proportional
More informationEEE 480 LAB EXPERIMENTS. K. Tsakalis. November 25, 2002
EEE 480 LAB EXPERIMENTS K. Tsakalis November 25, 2002 1. Introduction The following set of experiments aims to supplement the EEE 480 classroom instruction by providing a more detailed and handson experience
More informationProcess Identification for an SOPDT Model Using Rectangular Pulse Input
Korean J. Chem. Eng., 18(5), 586592 (2001) SHORT COMMUNICATION Process Identification for an SOPDT Model Using Rectangular Pulse Input Don Jang, Young Han Kim* and Kyu Suk Hwang Dept. of Chem. Eng., Pusan
More informationStep input, ramp input, parabolic input and impulse input signals. 2. What is the initial slope of a step response of a first order system?
IC6501 CONTROL SYSTEM UNITII TIME RESPONSE PARTA 1. What are the standard test signals employed for time domain studies?(or) List the standard test signals used in analysis of control systems? (April
More informationCHAPTER 1 Basic Concepts of Control System. CHAPTER 6 Hydraulic Control System
CHAPTER 1 Basic Concepts of Control System 1. What is open loop control systems and closed loop control systems? Compare open loop control system with closed loop control system. Write down major advantages
More informationIntroduction. Performance and Robustness (Chapter 1) Advanced Control Systems Spring / 31
Introduction Classical Control Robust Control u(t) y(t) G u(t) G + y(t) G : nominal model G = G + : plant uncertainty Uncertainty sources : Structured : parametric uncertainty, multimodel uncertainty Unstructured
More informationDynamics and PID control. Process dynamics
Dynamics and PID control Sigurd Skogestad Process dynamics Things take time Step response (response of output y to step in input u): k = Δy( )/ Δu process gain  process time constant (63%)  process time
More informationIntro to Frequency Domain Design
Intro to Frequency Domain Design MEM 355 Performance Enhancement of Dynamical Systems Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University Outline Closed Loop Transfer Functions
More informationCONSIM  MS EXCEL BASED STUDENT FRIENDLY SIMULATOR FOR TEACHING PROCESS CONTROL THEORY
CONSIM  MS EXCEL BASED STUDENT FRIENDLY SIMULATOR FOR TEACHING PROCESS CONTROL THEORY S. Lakshminarayanan, 1 Rao Raghuraj K 1 and S. Balaji 1 1 Department of Chemical and Biomolecular Engineering, 4 Engineering
More informationMAS107 Control Theory Exam Solutions 2008
MAS07 CONTROL THEORY. HOVLAND: EXAM SOLUTION 2008 MAS07 Control Theory Exam Solutions 2008 Geir Hovland, Mechatronics Group, Grimstad, Norway June 30, 2008 C. Repeat question B, but plot the phase curve
More informationAPPLICATIONS FOR ROBOTICS
Version: 1 CONTROL APPLICATIONS FOR ROBOTICS TEX d: Feb. 17, 214 PREVIEW We show that the transfer function and conditions of stability for linear systems can be studied using Laplace transforms. Table
More informationRichiami di Controlli Automatici
Richiami di Controlli Automatici Gianmaria De Tommasi 1 1 Università degli Studi di Napoli Federico II detommas@unina.it Ottobre 2012 Corsi AnsaldoBreda G. De Tommasi (UNINA) Richiami di Controlli Automatici
More informationQuanser NIELVIS Trainer (QNET) Series: QNET Experiment #02: DC Motor Position Control. DC Motor Control Trainer (DCMCT) Student Manual
Quanser NIELVIS Trainer (QNET) Series: QNET Experiment #02: DC Motor Position Control DC Motor Control Trainer (DCMCT) Student Manual Table of Contents 1 Laboratory Objectives1 2 References1 3 DCMCT Plant
More informationChapter 5 The SIMC Method for Smooth PID Controller Tuning
Chapter 5 The SIMC Method for Smooth PID Controller Tuning Sigurd Skogestad and Chriss Grimholt 5.1 Introduction Although the proportionalintegralderivative (PID) controller has only three parameters,
More informationSinusoidal Forcing of a FirstOrder Process. / τ
Frequency Response Analysis Chapter 3 Sinusoidal Forcing of a FirstOrder Process For a firstorder transfer function with gain K and time constant τ, the response to a general sinusoidal input, xt = A
More informationIMPROVED TECHNIQUE OF MULTISTAGE COMPENSATION. K. M. Yanev A. Obok Opok
IMPROVED TECHNIQUE OF MULTISTAGE COMPENSATION K. M. Yanev A. Obok Opok Considering marginal control systems, a useful technique, contributing to the method of multistage compensation is suggested. A
More information( ) Frequency Response Analysis. Sinusoidal Forcing of a FirstOrder Process. Chapter 13. ( ) sin ω () (
1 Frequency Response Analysis Sinusoidal Forcing of a FirstOrder Process For a firstorder transfer function with gain K and time constant τ, the response to a general sinusoidal input, xt = A tis: sin
More information100 (s + 10) (s + 100) e 0.5s. s 100 (s + 10) (s + 100). G(s) =
1 AME 3315; Spring 215; Midterm 2 Review (not graded) Problems: 9.3 9.8 9.9 9.12 except parts 5 and 6. 9.13 except parts 4 and 5 9.28 9.34 You are given the transfer function: G(s) = 1) Plot the bode plot
More informationClass 27: Block Diagrams
Class 7: Block Diagrams Dynamic Behavior and Stability of ClosedLoop Control Systems We no ant to consider the dynamic behavior of processes that are operated using feedback control. The combination of
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 informationEE 468 Control System Laboratory Supporting Materials and Experiments
EE 468 Control System Laboratory Supporting Materials and Experiments Khosrow Rad Helen Boussalis DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING CALIFORNIA STATE UNIVERSITY, LOS ANGELES ECP Systems, Inc
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 informationES205 Analysis and Design of Engineering Systems: Lab 1: An Introductory Tutorial: Getting Started with SIMULINK
ES205 Analysis and Design of Engineering Systems: Lab 1: An Introductory Tutorial: Getting Started with SIMULINK What is SIMULINK? SIMULINK is a software package for modeling, simulating, and analyzing
More informationRotary Motion Servo Plant: SRV02. Rotary Experiment #01: Modeling. SRV02 Modeling using QuaRC. Student Manual
Rotary Motion Servo Plant: SRV02 Rotary Experiment #01: Modeling SRV02 Modeling using QuaRC Student Manual SRV02 Modeling Laboratory Student Manual Table of Contents 1. INTRODUCTION...1 2. PREREQUISITES...1
More informationRobust Control 3 The Closed Loop
Robust Control 3 The Closed Loop Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University /2/2002 Outline Closed Loop Transfer Functions Traditional Performance Measures Time
More informationExperiment # 5 5. Coupled Water Tanks
Experiment # 5 5. Coupled Water Tanks 5.. Objectives The CoupledTank plant is a TwoTank module consisting of a pump with a water basin and two tanks. The two tanks are mounted on the front plate such
More informationMEM 355 Performance Enhancement of Dynamical Systems
MEM 355 Performance Enhancement of Dynamical Systems Frequency Domain Design Harry G. Kwatny Department of Mechanical Engineering & Mechanics Drexel University 5/8/25 Outline Closed Loop Transfer Functions
More information(a) Find the transfer function of the amplifier. Ans.: G(s) =
126 INTRDUCTIN T CNTR ENGINEERING 10( s 1) (a) Find the transfer function of the amplifier. Ans.: (. 02s 1)(. 001s 1) (b) Find the expected percent overshoot for a step input for the closedloop system
More informationCALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems
CDS 101 1. Åström and Murray, Exercise 1.3 2. Åström and Murray, Exercise 1.4 3. Åström and Murray, Exercise 2.6, parts (a) and (b) CDS 110a 1. Åström and Murray, Exercise 1.4 2. Åström and Murray, Exercise
More informationResearch Article. World Journal of Engineering Research and Technology WJERT.
wjert, 2015, Vol. 1, Issue 1, 2736 Research Article ISSN 2454695X WJERT www.wjert.org COMPENSATOR TUNING FOR DISTURBANCE REJECTION ASSOCIATED WITH DELAYED DOUBLE INTEGRATING PROCESSES, PART I: FEEDBACK
More information