EI6801 Computer Control of Processes Dept. of EIE and ICE

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1 Unit I DISCRETE STATE-VARIABLE TECHNIQUE State equation of discrete data system with sample and hold State transition equation Methods of computing the state transition matrix Decomposition of discrete data transfer functions State diagrams of discrete data systems System with zero-order hold Controllability and observability of linear time invariant discrete data system Stability tests of discrete-data system State Observer - State Feedback Control. Part A 1. Write the state equation for discrete data system. ( ) ( ) ( ) State Equation ( ) ( ) ( ) Output Equation 2. Draw the state diagram of discrete data system. U(k) ) X(k+1 X(k) B )) Z -1 C A y(k) 3. Write the State transition equation of a discrete system. 1 1 A k Z { zi A) z} 4. Write the solution of State transition matrix of a discrete system. X ( k) Z { zi A) z} X (0) Z { zi A) BU( z)} 5. List out the Methods of computing the state transition matrix. 1. Using X transform, 2. Canonical transformation, 3. Cayley- Hamilton theorem. 6. State the properties of State transition matrix of a discrete system (0) ( k) ( k) D ( kk ) 0 ( k, k0) ( k k0) A, where k k0 7. A discrete time system is described by the difference equation, y(k+2)+ 3y(k+1)+5y(k)=u(k). determine the transfer function of the system. Solution: y(k+2)+ 3y(k+1)+5y(k)=u(k) taking Z transform, Z 2 Y(z)+3zY(z)+6Y(z)=U(z) (Z 2 +3z+6)Y(z)= U(z) Y( z) 1 2 U( z) z 3z 6 8. Write down the equation for obtaining transfer function from discrete state model. Y( z) c( zi A) B D U( z) 9. Draw the block diagram zero order hold sampled data control system. T y(k) r(t) + ZOH G(s) e(k) c(t) St. Joseph s College of Engineering 3

2 10. What are the advantages of state space modeling using physical variable? The state variable can be utilized for the purpose of feedback. The implementation of design with state variable feedback becomes straight forward. The solution of state equation gives time variation of variables which have direct relevance to the physical system. 11. Define controllability. For the linear system ( ) ( ) ( ) ( ) ( ) ( ), if there exists an input ( ) with a finite positive integer, which transfers the initial state ( ) to the state at, the state is said to be controllable. If all initial states are controllable, the system is said to be completely controllable. Otherwise, the system is said to be uncontrollable. 12. How the controllability of the discrete system is checked? The necessary and sufficient condition for the system ( ) ( ) ( ) ( ) ( ) to be completely controllable is that the controllability matrix has the rank equal to. 13. Define observability of a system. For the linear system x( ) ( ) ( ) ( ) ( ) ( ), if the knowledge of input signal ( ) and the output ( ) with a finite positive integer, suffices to determine the state ( ) to the state is said to be observable. If all initial state are observable, the system is said to be completely observable. Otherwise, the system is said to be unobservable. 14. How the observability of the discrete system is checked? The necessary and sufficient condition for the system ( ) ( ) ( ) ( ) ( ) to be completely observable is that the observability matrix has the rank equal to. 15. State the necessary condition for Jury s stability test Consider the characteristic polynomial ( ) The necessary condition for stability is ( ) ( ) ( ) 16. How many rows are formed in Jury s table and what are the sufficient conditions to be checked from this table for stability? rows, where is the order of the system. 17. For the characteristic polynomial ( ), find the stability of the system. Necessary condition for stability, ( ) and ( ) { According to the necessary conditions the system may be stable. 18. What is Bilinear transformation? Bilinear transformation maps the interior of the unit circle in the z-plane into the left of plane. maps the interior of the unit circle in the plane into the left of plane 19. Use the bilinear transformation to check the stability for the characteristics equation ( ) Such a transformation (or mapping) is provided by the bilinear transformation Row 1: The elements in the first column are positive. So, the system is stable. St. Joseph s College of Engineering 4

3 20. What is the need for state observer? In certain systems the state variables may not be available for measurement and feedback. In such situations we need to estimate the un-measurable state variables from the knowledge of input and output. Hence the state observer is employed which estimate the state variables from the input and output of the system. The estimated state variable can be used for feedback to design the system by pole placement. 21. How control system design is carried in state space? In state space design of control system, any inner parameter or variable of a system are used for feedback to achieve the desired performance of the system. The performance of the system is related to the location of closed loop poles. Hence in state space design the closed loop poles are placed at the desired locations by means of state feedback through an appropriate state feedback gain matrix, K. 22. What is the necessary condition to be satisfied for design using state feedback? The state feedback design requires arbitrary pole placement to achieve the desired performance. The necessary and sufficient condition to be satisfied for arbitrary pole placement is that the system be completely state controllable. 23. How is pole placement done by state feedback in a sampled data system? Consider the system, ( ) ( ) ( ) Assume that there is only one input signal. If the system is reachable there exists a linear feedback that gives a closed-loop system with the characteristic polynomial ( ). The feedback is given by ( ) ( ). 24. State the duality between controllability and observability? The concepts of controllability and observability are dual. The principle of duality states that a system is completely state controllable if and only of its dual system is completely observable or vice versa. 25. What is the advantage and disadvantage of kalman s test for observability? Advantage: Calculation is very simple. Disadvantage: non-observable state variables cannot be determined. Unit II Part B 1. Explain sample data control system with neat sketch. 2. Derive the solution for discrete state transition matrix. 3. (i) Check whether the system is completely controllable. [ ] [ ] [ ] [ ] ( ) (ii) Determine the observability of the given system. [ ] [ ] [ ] [ ] ( ) [ ] 4. Investigate the controllability and observability of the following system ( ) [ ] ( ) [ ] ( ) ( ) ( ) 5. Explain Jury s stability test. St. Joseph s College of Engineering 5

4 6. Consider the discrete time unity feedback control system(with sampling period T=1 sec) ( ) whose open loop transfer function is given by ( ). Determine the range ( )( ) of gain for the stability by using Jury s stability test. 7. Determine the stability of the sampled data control system whose open loop pulse transfer function using Schur-Cohn stability criterion. z A(z) 2.45z 2.45z 8. Consider the system shown in figyre. Find out the range of K for which the system is stable usijng Jury s stability method. 9. Using Jury s stability test, check if all the roots of the following characteristic equation lie within the unity circle. 10. Consider a plant defined by the following state variable model ( ) ( ) ( ) ( ) ( ) ( ) Where [ ] [ ]. Design a predictive observer for the estimation of the state vector. The observer error poles are required to lie at. 11. A discrete time regulator has the plant ( ) [ ] ( ) [ ] ( ) Design a state feedback controller which will place the closed loop poles at 12. Consider the discrete time system ( ) ( ) ( ) ( ) ( ) Where [ ] [ ] (i) Show that the system is completely controllable and observable. (ii) Determine a suitable state feedback controller such that the closed loop system has poles 13. A single input system is described by the following state equation [ ] [ ] Design a state feedback controller which will give closed loop poles at block diagram of the resulting closed loop system.. Draw a UNIT II SYSTEM IDENTIFICATION Non Parametric methods:-transient analysis Frequency analysis correlation analysis Spectral analysis Parametric methods:- Least square method Recursive least square method. Unit II Part A St. Joseph s College of Engineering 6

5 1. What is meant by mathematical modelling of physical system? Mathematical model is a way of describing the relationship between the input, output and error. 2. What are the advantages of mathematical model? Mathematical model needs (i) To analyze the stability of the system. (ii) to design a suitable controller (iii) To optimize the economic performance of a plant 3. How the mathematical modelling of higher order process obtained? The mathematical modelling of higher order process are obtained in three ways N first order processes in series Processes with dead time Processes with inverse response. 4. What System identification? System identification is the process of building mathematical models of the dynamical systems based on the observed data from the systems. 5. What are the types of system identification? Non-parametric methods and Parametric methods 6. What are the non-parametric methods of system identification? o Transient analysis (step or impulse response analysis) o Frequency analysis (sinusoidal response analysis) o Correlation analysis (white noise response analysis) o Spectral analysis 7. What are the parametric methods of system identification? Least square Maximum likelihood 8. What is Least square method? The method of least squares is a standard approach in regression analysis to the approximate solution of over determined systems, i.e., sets of equations in which there are more equations than unknowns. "Least squares" means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation. 9. What is maximum likelihood estimation? Maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model given observations, by finding the parameter values that maximize the likelihood of making the observations given the parameters. 10. What are the properties of maximum likelihood estimation? Consistency, Asymptotic normality, Efficiency 11. What are the Advantages and drawbacks non-parametric system identification? Advantage: Easy to apply Drawbacks: The derived model is not accurate Sensitive to noise 12. What are general steps involved in system identification? The steps involved in system identification are: _ Collection of input-output data _ Choosing of a set of candidate models and _ Determination of best model in the set St. Joseph s College of Engineering 7

6 13. Distinguish mathematical modeling and system identification. Mathematical modelling They are valid over a wide range of operating conditions and inputs St. Joseph s College of Engineering 8 System identification They are valid only for a certain working point and certain types of inputs. Easy to construct and use Hard to construct and use 14. What is PRBS? A pseudorandom binary sequence (PRBS) is a binary sequence that, while generated with a deterministic algorithm, is difficult to predict and exhibits statistical behavior similar to a truly-random sequence. PRBS are used in telecommunication, encryption, simulation, correlation technique and time-offlight spectroscopy. 15. What is the reasons for using PRBS for system identification? Usually PRBS is applied for system identification for the following reasons: _ Easy to generate _ Resembles white noise as far as spectral properties are concerned _ PRBS signal with prescribed spectral properties can be easily generated by various forms of linear filtering available _ Cross-correlation of a PRBS signal with another signal needs only addition operations. (multiplications are not required) 16. Distinguish between on line and off line method of system identification Online estimation algorithms estimate the parameters of a model when new data is available during the operation of the model. In offline estimation, you first collect all the input/output data and then estimate the model parameters. Parameter values estimated using online estimation can vary with time, but parameters estimated using offline estimation do not. 17. What are the white, gray and black box models? White-box model based on first principles, e.g. a model for a physical process from the Newton equations, but in many cases such models will be overly complex and possibly even impossible to obtain in reasonable time due to the complex nature of many systems and processes. Model sets with these adjustable parameters comprise so-called grey-box models. in control applications, it usually suffices to use linear models which do not necessarily refer to the underlying physical laws and relationships of the process. These models are generally called blackbox models. 18. What is stochastic system? A stochastic system is one which cannot be expressed precisely but can be expressed with the help of statistical data. 19. What is deterministic system? A deterministic system on the other hand can be expressed precisely. Usually deterministic systems are encountered in case of servo systems. Stochastic systems are encountered in case of regulator systems 20. Give example for stochastic process. speech, audio and video, medical data such as a patient's EKG, EEG, blood pressure or temperature Unit II Part B 1. Derive the Recursive least square algorithm for estimating the parameters of AR model

7 2. Derive the Recursive least square algorithm for estimating the parameters of ARX model 3. Derive the expression for Finite Impulse Response Model (FIR model) 4. Derive the Recursive least square algorithm for estimating the parameters of ARMA model 5. Derive the Recursive least square algorithm for estimating the parameters of ARMAX model 6. Derive the Recursive least square algorithm for estimating the parameters of ARIMA model 7. Explain in detail about fixed memory algorithm. 8. Explain in detail about the minimum variance method 9. Derive the algorithms equations to estimate the parameters using recursive least square method. 10. Write notes on Extended Recursive least squares 11. Explain in detail about Maximum likelihood UNIT III DIGITAL CONTROLLER DESIGN Review of z-transform Modified of z-transform Pulse transfer function Digital PID controller Dead-beat control and Dahlin s control Smith predictor Digital Feed-forward controller IMC State Feedback Controller - LQG Control Unit III Part A 1. Define Z-transform Z- transform can be defined as X(Z)= x(n)z -n, n=- 2. DefineROC The region of convergence (ROC) of X(Z) the set of all values of Z for which X(Z) attain final value. 3. Z transform of a unit step function. F(t)={0 t<0 u(t) t 0 By definition, Z{u(t)}=F(z)= u(nt).z -n 4. What is the use of modified Z-Transform? Z-transform method enables us to determine the transient response of sampled data controlled systems only at the sampling instants, in-order to obtain the value of response between the sampling instants; modified Z-transforms are useful. They are also useful in analysing sampled data control systems containing transportation lag (dead time). 5. Define Pulse Transfer Function The transfer function of a linear system is given by Z transform of its impulse response. Transfer function of Linear system is also called Z transfer function or pulse transfer function. Let h(k)=impulse response of system Z transform of h(k)=z{h(k)}=h(z) 6. Input-Output relation of a sample data system is described by the equation C(k+2)+3C(k+1)+4C(k)=r(k+1)-r(k).Determine its pulse transfer function. Assume Zero initial conditions, z 2 C(z)-z 2 C(0)-zC(1)+z 2 C(z)+3Zc(Z)+4C(z)=zR(z)-R(z) simplifying and rewriting ; (z 2 +3z+4)C(z)=(z-1)R(z) St. Joseph s College of Engineering 9

8 C(z)/R(z)=z-1/z 2 +3z+4 7. Define pole placement. Placing the poles or eigenvalues of the closed-loop system at specified locations. Poles can be arbitrarily placed if and only if the system is controllable. Pole placement is easier if the system is given in controllable form. 8. State Deadbeat algorithm An algorithm that requires the closed loop response to have a finite settling time, minimum rise time,and zero steady state error is referred to a specification that satisfies these criteria is C(Z)/R(Z)=Z -1 Control algorithm is D(Z)=1/G(z)*Z -1 /I-Z Sketch the Block Diagram of a feed forward controller. 10. What is a LQG controller. The LQG controller is simply the combination of a Kalman filter, i.e. a linear quadratic estimator (LQE), with a linear quadratic regulator (LQR). The separation principle guarantees that these can be designed and computed independently. LQG control applies to both linear time-invariant systems as well as linear time-varying systems. This is given by the control law u=-kx 11. Write the position and velocity form of discrete PID control. u(k)=u o +k c ( ) ( )+ (( ( ) ( ))]-position form ( ) ( ) ( ) ( ) ( ) ( ) ( ) -velocity form 12. Perform the stability analysis for digital control systems For a standard discrete feedback control system, the closed loop system is stable if the poles of the closed-loop transfer function are all inside the unit circle. The closed loop transfer function is g cl (z)=g c (z)g p (z)/1+g c (z)g p (z) so the roots are 1+g c (z)g p (z)=0. Must be less than 1 in magnitude 13. What is a full order and reduced order state observer? If the state observer estimates all the state variables of the system, regardless of whether some state variables are available for direct measurement, then it is called as a full order state observer, however if accurate measurements of certain states are possible, we may estimate only the remaining states, and the accurately measured signals are then used directly for feedback. The resulting observer is called a reduced -order state observer 14. State Dahlins Algorithm. Dahlins algorithm specifies that the closed loop sampled data system behaves as a first order process with dead time.the response is given St. Joseph s College of Engineering 10

9 C(Z)/R(Z)=F(Z).G(Z) F(Z).Z -(N+1) Where,F(Z)=first order process with dead time N=no.of sampling periods in the process dead time D(z)=1/HGp(Z)*(1-α)z -(N+1) /(1- αz-1)-(1-α)z -(N+1) 15. What are the various tuning parameters chosen for designing MPC. The following are the parameters: 1. Sampling period t and model horizon N. 2. Control M and prediction P horizons 3. Weighting Matrices, Q and R 4. Reference Trajectory i 16. What is dead time or transportation lag or distance velocity lag? Whenever the input variable of a system changes, there is a time interval (short or long) during which no effect is observed on the outputs of the system. This time interval is called as dead time 17. Explain the Smith Predictor Algorithm. Smith's strategy consists of an ordinary feedback loop plus an inner loop that introduces two extra terms directly into the feedback path. The first term is an estimate of what the process variable would look like in the absence of any disturbances. The second element represents nothing but the deadtime. The deadtime-free element is generally implemented as an ordinary differential or difference equation that includes estimates of all the process gains and time constants. The second element of the model is simply a time delay The Smith Predictor works to control the modified feedback variable (the predicted process variable with disturbances included) rather than the actual process variable. If it is successful in doing so, and if the process model does indeed match the process, then the controller will simultaneously drive the actual process variable towards the set-point, whether the set-point changes or a load disturbs the process. The dead time becomes irrelevant. 18. Draw the generalized block diagram of a Model Predictive control. 19. Obtain the pulse transfer function G(z) of the system shown below, where G(s) is given by G(s)=1/s(s+1) St. Joseph s College of Engineering 11

10 20. Explain optimal control synthesis. Find optimal control for any initial conditions at any point in time apply control that is optimal now, based on the current state. This is feedback control. example: LQG for linear systems, Gaussian noise, quadratic performance index. Analytically solvable problem. Simplified model, toy problems, and conceptual building block. Unit-III Part B 1. i)determine the Z transform of X(s)=1/s(s+1) ii)determine the Z transform of X(s)=1/s 2 (s+1) 2. Determine the response of system shown in figure to a unit step change in set point. Assume t=1sec,and D(z) is a control algorithm with the value of 2 and N=3 Set.pt T + T D(z) Gho(s) Gp(s) St. Joseph s College of Engineering 12 - Given R(S) Gho(s)=1-e -st /s Gp(s)=e- 3.5s /s+5 N=3 T=1sec D(z)=2 3. Determine the response of the system to a unit step change in set point. Assume T=0.5, and D(z) is a PI controlled algorithm and with Kc=0.43,Ti=1.57.The closed loop pulse transfer function of the system is C(z)/R(z)=D(z).Gh o G p (z);g p (s)=e -0.76s /0.4s+1 4. Gp(s)=e-1.46s/3.34s+1; Design a Dahlins algorithm with sampling period of 1 sec. 5. Gp(s)=10e-2s/0.2s+1; where T=1sec, Design a Dahlins Algorithm. 6. Obtain the deadbeat control law for the given below Gp(s)=1/0.4s+1, where sampling period, T=1sec 7. Design a deadbeat algorithm where Gp(s)=e -0.8s /0.6s+1, with sampling period of T=0.4sec 8. i)write short notes on IMC(8) ii)write short notes on MPC(8) 9. Explain the PID design procedure using IMC substantiating with designing a IMC based PID control for first order and second order process. 10. What is transportation lag. Design a Smith Predictor for controlling the delay time T

11 UNIT IV MULTI-LOOP REGULATORY CONTROL Multi-loop Control - Introduction Process Interaction Pairing of Inputs and Outputs -The Relative Gain Array (RGA) Properties and Application of RGA Multi loop PID Controller Biggest Log Modulus Tuning Method De coupler Unit IV Part A 1. Define multi-loop control. Multi-loop control is a control system composed of several interacting and noninteracting control loops. For such a control system there is more than one possible control configuration for a MIMO process. 2. What is process interaction? Process interaction is defined as the regulatory action of a control loop deregulates the output of another loop which in turn takes control action to compensate for the variations in its controlled output, disturbing at the same time the output of the first loop. 3. Explain the input-output pairing problem. Consider the matrix vector notation, where y(s) is a vector of n inputs and u(s) is a vector y1( s) g11( s) g1 m( s) u1( s) of m outputs, y( s) G( s) u( s); where each output y ( s) g ( ) ( ) ( ) n n1 s gnm s um s can be represented by, St. Joseph s College of Engineering 13 m y ( s) g ( s) u ( s). The pairing problem arises as to which i j ij j input u j should be paired with output y i to form a SISO control loop. 4. What is a MIMO system? Explain with an example. A MIMO system is a multi-input and multi-output system for which more than one control strategy can be administered. Eg: Flash drum unit in which the inputs are feed and vapour while the outputs are steam and liquid. 5. What is decoupling? When the designer is confronted with two strongly interacting control loops decoupling is used to render two non-interacting loops in the system. 6. What is the function of a decoupler? The purpose of the decoupler is to cancel the interaction effects between the two loops and thus render two non-interacting control loops. 7. What is RGA? The relative-gain array provides a methodology where we select pairs of input and output variables in order to minimize the interaction among resulting loops. It is a square matrix. For a 2x2 system, the that contains individual relative gain as elements, that is 1 2 RGA is Define relative gain. The relative gain (λ ij ) between input j and output I is defined as follows; y i u j u k k λ ij = ij y i u j ij j yk ki

12 9. Give the applications of Relative Gain Array. RGA is used to determine variable pairing, in which the inputs and outputs are paired. 10. What is failure sensitivity? When tuning a set of SISO controllers to form a multivariable SISO strategy, it is important to consider the failure sensitivity of the system which involves putting one of the loops in manual control. 11. Explain sum of rows and columns property of an RGA matrix. 1 2 RGA is given by, this equation yields the flowing relationships, , then for a 2x2 system, only one relative gain must be calculated for the entire array, What is open loop static gain? Considering a system with inputs m 1 and m 2, and y 1 be the previous steady state, then the y 1 open loop static is given by m where 1 m What is relative gain? The ratio of the two open-loop gains defines the relative gain λ 11 between output y 1 and y1 m1 m 2 input m 1, which provides a useful measure of interaction; 11 y m St. Joseph s College of Engineering y2 14. What is partial decoupling? Despite the fact when two decouplers are required, of only one is used, then the strategy is called as partial decoupling. This partial decoupler allows the interaction to travel in one direction. 15. What is static decoupling? Steady state or static decoupling are designed using steady state models. For severely interacting loops static decoupling are essential rather than no decoupling. 16. What is the result of dynamic interaction? - Analyses additional interaction effects above the steady state - Observes the degradation in control system performance - Use a true multivariable control system design rather than separate SISO controllers - Under severe interaction, one of the loops can be closed. 17. For the given RGA, give the variable pairing We pair y 1 with u 2 and y 2 with u Define BLT method. This method called the biggest log modulus tuning method was proposed by Luyben. The method achieves the conservative objectives of arriving at reasonable controller settings. The BLT algorithm yields a value of F, which gives a reasonable compromise between stability and performance in multivariable systems. 19 What are the degrees of freedom with respect to multiloop control? The maximum number of independent controlled variables in a processing system is equal to the number of degrees of freedom minus the number of externally specified variables. The degrees of freedom are the independent variables that completely define a process. 20 What are the criteria to select the best loop configuration? 1. Choose the manipulation that has a direct and fast effect on a controlled variable.

13 2. Choose the couplings so that there is little dead time between every manipulation and the corresponding controlled variable 3. Select the couplings so that the interaction of the control loops is minimal. Unit IV Part B 1. Explain in detail the biggest log modulus tuning method. 2. What is RGA? Explain with examples and the properties. 3. How is RGA useful for determination of variable pairing? 4. Write in detail about RGA and selection of loops. 5. Enumerate on the design of non-interacting control loops. 6. Explain about interaction of control loops. 7. Explain multiloop PID controller. 8. Write in detail about the general pairing problem. 9. What is decoupling? Explain the types of decoupling. 10. Derive RGA for three input- three output system. 11. Derive RGA for n input- n output system. UNIT V MULTIVARIABLE REGULATORY CONTROL Introduction to Multivariable control Multivariable PID Controller -Multivariable IMC Multivariable Dynamic Matrix Controller Multivariable Model Predictive Control Generalized Predictive Controller Implementation Issues. Unit V Part A 1. What is multivariable control? A multivariable process has more than one input variables or more than one output variables. To each variable (process output variable) which is to be controlled a setpoint is given. To control these variables a number of control variables are available for manipulation by the controller function. 2. What are the difficulties in multivariable control? a) Multivariable processes can be difficult to control if there are cross couplings in the process, that is, if one control variable gives a response in several process output variables. b) There are mainly two problems of controlling a multivariable process if these cross couplings are not counteracted by the multivariable controller. A change in one setpoint will cause a response in each of the process output variables, not only in the output variable corresponding to the setpoint. 3. What are the features of full multivariable controller? The full multivariable controller (centralized controller) will give satisfactory response for multivariable process. However, the multivariable controller system requires n x n controllers. This controller can be designed by assuming the controller structure as a full matrix with each element as specific controller. 4. How multivariable PID controller is differing from multi-loop PID? The multi loop controller design is based on decentralized method (i.e splitting the multiloop variable into various single loop and controller is designed accordingly) whereas multivariable controllers is based on centralized method. The interaction between all manipulated and control variables are taken into consideration. 5. List few methods of tuning of multivariable PID controller? Davison method, Maciejowski method, Tanttu and Lieslehto method. St. Joseph s College of Engineering 15

14 6. Write the expression for Maciejowski method of tuning for PI controller. The controller parameter for PI controller is K [ G( s j )], K [ G( s 0)] where G ( s 0)] is called rough matrix and c b and are the fine tuning parameters. I b is the desired bandwidth of the system. 7. What is Internal Model Control? IMC is one kind of controller with a single tuning parameter (the IMC filter λ). For a system that is minimum phase λ is equivalent to a closed loop time constant (speed of response) 8. Compare IMC and PID controller. The IMC is based on explicitly process model for control system design whereas the standard feedback control design is based on implicit process model. The tuning parameters of PID controllers are often tweaked based on process model. But the IMC parameter formulation the parameter is part of process transfer function. 9. Briefly explain about multivariable IMC. A multivariable internal model control is a control system introduced an internal model in which an internal model and actual object controlled is parallel formation, and the output feedback of the system is a feedback of disturbance estimated. Foreword feedback compensation proposed for removing out minimum phase of the model which takes equivalent inverse of minimum phase part to make the system outputs track inputs change. 10. Draw the block diagram of multivariable IMC. Where R denotes reference input, GIMC denotes internal model controller, GD denotes foreword feedback compensation device, GP denotes transfer function of actual process, GM denotes equivalent system model of the actual process decoupled, G(s) denotes interference channel transfer function matrix, GC denotes system transfer function matrix, sf )( denotes diagonal matrices interference input, Y(s) denotes system output. 11. Briefly explain about Dynamic Matric control The DMC algorithm technique to predict the future output of the system as a function of the inputs and disturbances. This prediction capability is necessary to determine the optimal future control inputs. 12. Write the objective function for multivariable DMC. For a system with S controller outputs and R measured process variables, the multivariable DMC quadratic performance objective function has the form a. St. Joseph s College of Engineering 16

15 13. What are the steps involved in implementing DMC on a process? a) Develop a discrete step response model with length N based on sample time. b) Specify the prediction and control horizon c) Specify the weighting on the control action. d) All calculation assumes deviation variable form to convert physical units. 14. Draw the schematic of Model Predictive Control. 15. List the advantages of Model Predictive Control. Model predictive control offers several important advantages: the process model captures the dynamic and static interactions between input, output, and disturbance variables, constraints on inputs and outputs are considered in a systematic manner, the control calculations can be coordinated with the calculation of optimum set points, and Accurate model predictions can provide early warnings of potential problems. 16. List various models used for designing MPC algorithm. Finite step response, finite impulse response and state space model 17. What are the objectives of an MPC controller? The overall objectives of an MPC controller have been summarized as Prevent violations of input and output constraints. Drive some output variables to their optimal set points, while maintaining other outputs within specified ranges Prevent excessive movement of the input variables. Control as many process variables as possible when a sensor or actuator is not available. 18. What is Generalized Predictive Control? The generalized predictive control (GPC) is a general purpose multi-step predictive control algorithm for stable control of processes with variable parameters, variable dead time and a model order which changes instantaneously. GPC adopts an integrator as a natural consequence of its assumption about the basic plant model. St. Joseph s College of Engineering 17

16 19. Draw the basic structure of GPC. 20. List the various implementation issues in multivariable controller design. Analog implementation (multi-loop, centralized and decentralized) Digital implementation (hardware, scheduling, data acquisition and control algorithm) User interface (I/O, plant wise implementation) Unit V Part B 1. Explain with suitable example the importance and challenges in multivariable control. 2. Discuss the various conventional centralized controller procedures for multivariable process. 3. Given (K p G p ) 11 = 1/[(6s+1) (3s+1)]; (K p G p ) 12 = 1/(4s+1) ; (K p G p ) 21 = 2/(3s+1); (K p G p ) 22 = 1/[(4s+1) (2s+1)]; design a multivariable controller by using Davison method. Evaluate the time response of the closed loop system for step input changes in the set point. 4. Explain the design process of IMC controller design with (i) an all pass filter is used, (ii) the controller is strictly proper. 5. Design DMC for the van de vusse reactor problem. The state space model of reactor is given as A = [ ; ], B = [7; ], C = [0 1], D = [0]. 6. Summarize various steps involved in DMC controller design. Derive the expression for an objective function for controller design. 7. Discuss the tuning methods of multivariable model predictive control and explain any one method. 8. Derive the expression for step response model based predictive control. 9. Briefly explain about Generalized Predictive control with an example. 10. Enumerate various implementation issues in multivariable control and explain in detail St. Joseph s College of Engineering 18