05444 Process Control System Design LECTURE 6: SIMO and MISO CONTROL Daniel R. Lewin Department of Chemical Engineering Technion, Haifa, Israel 6 - Introduction This part of the course explores opportunities to improve the performance of simple SISO control: Additional process outputs (measurements) may be available these cases are referred to as SIMO (single input, multiple outputs) For example, when controlling a reactor using the flow of cooling water, both the reactor temperature and the temperature of the coolant effluent can be measured. More than one process input which affects the process output can be manipulated or measured - these cases are referred to as MISO (multiple inputs, single output) For example, the temperature of the reactor feed (a disturbance) can be measured, and the coolant flow rate can be manipulated. Both of these affect the reactor temperature. 6-2
Objectives On completing this section, you should be able to: Identify processing situations that require special treatment such as cascade, override, auctioneering, feedforward and ratio control. Correctly design a cascade control system. Correctly design a feedforward control system. You should be able to select the best from among the above options in a given design situation. 6-3 SIMO Systems In these control systems, with only one manipulated variable, a number of process outputs (measurements) may be available. These control systems include: Cascade control systems These involve one or more inner, slave loops, and an outer, master loop. Override systems Auctioneering systems 6-4 2
Cascade Control Objectives: To suppress disturbance d 2 before it influences primary variable y. The inner loop should be aggressive enough to eliminate the effect of these disturbances. To compensate for nonlinearities in the inner loop (e.g. valve hysteresis). Flow Valve hysteresis Valve Position 6-5 Cascade Control (Cont d) p2c 2 Analysis. Inner loop: y2 = d2 + ys 2 + pc 2 2 + pc 2 2 = d + L y 2 2 S2 pd 2 + d pl2c Outer loop: y = + ys + pl2c + pl2c Design Procedure. Design outer loop first, as is the inner loop transfer function is L 2 = i.e. assume BW(L 2 ) >> BW(L ). Tune outer loop filter to meet performance specifications. Compute BW(L ). Then tune inner loop to be fast enough. 6-6 3
Cascade Control (Cont d) Design Procedure. Design outer loop first, as is the inner loop transfer function is L 2 = i.e. assume BW(L 2 ) >> BW(L ). Tune outer loop filter to meet stability and performance specifications. Compute BW(L ). Design inner loop to ensure: Robust stability BW(L 2 ) > 5-0 BW(L ). Proportional band of inner loop is reasonable and on-off control of inner loop is avoided. If any of the above are not satisfied, return to and increase the filter time constant of the outer loop. 6-7 Example Cascade Controllers Example. Vessel level control. Outer loop LC primary loop Inner loop FC slave loop Example. Reactor temperature control. Outer loop TC on T primary loop Inner loop TC on T J slave loop How does this cascade control system improve on the performance of a LC using the product valve? How does this cascade control system improve on the performance of a TC using F J? 6-8 4
Cascade Design - Class Exercise Design control systems for an exothermic reactor. Note that T responds to T J according to:.5 2s T( s) = e TJ ( s) 5s + Also, T J responds to F J and T J0 according to: k 0.02s 0.5 0.02s TJ( s) = e FJ( s) + e TJ0( s) s + s + The valve gain is uncertain, 0.5 k.5, a result of valve hysteresis. Design a cascade control system, limited to PIDs, that gives the fastest possible response of temperature to its set point, while being almost insensitive to step-like disturbances in T J0. Compare with the best SISO PID controller. 6-9 Cascade Design - Solution Single PID case. In this case, F J is used to control T directly. Thus the transfer function is:.5k 2.02s T( s) = e F J ( s),0.5 k.5 ( 5s + )( s + ) A Padé approximation for the delay term gives the model:.5(.0s + ) p ( s ) ( 5s + )(.0s + )( s + ) This is a third order transfer function. The most accurate second order approximation is:.5(.0s + ) p ( s ) = ( 5s + )(.0s + ) 0.666( 5s + ) The IMC controller is: q( s ) ( single PID) λ s + ( ) 6-0 5
Cascade Design - Solution Single PID case (Con d). Next, the multiplicative uncertainty is computed: 2.25 2.02s.5(.0s+ ) e ( 5s+ )( s+ ) ( 5s+ )(.0s+ ) m(s) =.5(.0s+ ) ( 5s+ )(.0s+ ) =.5 2.02s.0s+ e s+.0s+.0s+.0s+ m single loop The best BW attainable by a single PID controller, computed using MATLAB is ω c = 0.78 rad/min. Thus, set λ to.3 min. 6 - Cascade Design - Solution Cascade design. The transfer function seen by the outer loop controller is:.5 2s p( s) = e 5s + A Padé approximation for the delay term gives the model: m.5( s + ) p ( s ) ( 5s + )( s + ) 0.666( 5s + ) The IMC controller is: q( s ) λ s + ( ) m single loop cascade inner loop Next, the multiplicative uncertainty is computed as before, giving the approximate bandwidth, ω c =.48 rad/min. Thus, set λ to 0.5 min. 6-2 6
Cascade Design - Solution Cascade design (Cont d). To complete the design, the inner loop must be designed. The process seen by the inner loop controller is: k 0.02s p ( s) = e,0.5 k.5 s + The inner loop bandwidth must be 5-0 times larger than that of the outer loop. Let s shoot for 5 rad/min. The simplest inner loop controller would be a PI controller, based on the model: p ( s) = ( s + ). The IMC controller is: q( s) = ( s + ) ( λ s + ) 0.02s Here, the multiplicative uncertainty is: (s) =.5e This approximately limits the bandwidth to ω c = 35 rad/min! The cascade control system calls for an inner PI loop (λ = /5 min) and an outer PID loop (λ 2 = 0.5 min). This should respond about three times as fast as the best single loop PID controller. m 6-3 SIMULINK Simulation Model λ =.3 min K C = 5 Single-loop λ = 0.5 min Cascade SIMULINK model to simulate comparison between single-loop and cascade control 6-4 7
Cascade Design Simulation Results Servo response of single PID controller. Note the large effect of uncertainty on the responses, and the sluggish response; it cannot be faster! Servo response of cascade controller. Note that the inner loop almost eliminates the effect of uncertainty, and the significantly faster response. 6-5 Cascade Design Simulation Results Regulatory response of single PID controller. The effect of a disturbance in the cooling water feed temperature is rejected very sluggishly! Regulatory response of cascaded controller. The inner loop efficiently eliminates the effect of the same disturbance (by design). 6-6 8
Selective SIMO Control Several measured outputs are used to define one control action. Example. Override control for a boiler. The low selector switch (LSS) ensures that the most critical process variable is used to control the vapor product valve. Example. Auctioneering tubular catalytic reactor control. This ensures that the highest temperature is used for feedback control, regardless of its position. 6-7 MISO Systems These control systems are characterized by more than one process input, but only one output. Examples include, but are not limited to: Split-range control. In these systems, at least two distinct control variables are manipulated by the same controller, to regulate a single output variable. Feedforward control. Here, control action is computed on the basis of a prediction of the effect of a measured disturbance on the process output. As will be seen, feedforward control action is usually augmented to a feedback control system. 6-8 9
Split-range Control Example: Exothermic batch reactor control. If the controller needs to bring the reactor contents to ignition (by heating), and subsequently remove heat of reaction, a splitrange control configuration is called for. Several possible implementations are illustrated below. Discuss the advantages and disadvantages of each. U c U U c U h h 0 0 3 9 P 5 C (psig) 3 9 P 5 C (psig) 6-9 Two-DOF Controllers Assuming perfect model ( p = p): y = pq y d + d e = y y = pq y d S ( S ) ( )( ) S Thus, q cannot be designed to reject disturbance, d, and track setpoint y s, if these signals are of different type. However, 2-DOF controllers can be designed to tune separately for setpoint tracking and disturbance rejection = ( 2) S ( ) = ( ) ( ) e pqq y pq d e pq y pqq d S 2 6-20 0
Feedforward Control A better arrangement for disturbance rejection (assuming the disturbance is measured). pd + cp f y = d + pc pd Ideally, cf = p Problems. If p is NMF, c f as defined above can be unstable and/or noncausal (or both). The FF controller, c f, and the feedback controller, c, cannot be designed independently. 6-2 Feedforward Control (Cont d) IMC Feedforward Structure. Perfect model: p = p, p = p d d ( ) y = pq y + p + pq d s d f ( ) ( ) e = y y = pq y p + pq d s s d f Independent design of q and q f 6-22
Advantages. Acts before effect of disturbance is felt. 2. Good for NMP systems. 3. Does not affect stability.. Does not require disturbances to be measured. 2. Can be made robust to model errors. FB/FF: Pros and Cons Feedforward Control Feedback Control Disadvantages. Requires measurement of all disturbances. 2. Sensitive to process variations. 3. Requires good process models. 4. Cannot control open-loop unstable processes.. Only acts after disturbances effect output. 2. Performance poor for NMP systems. 3. May create instability. 6-23 Example of FB + FF Control Design a control system for an an exothermic reactor, using the coolant valve as the manipulated variable. The following measurements are available: () feed temperature, (2) reactor temperature, (3) coolant flow rate. FF compensation for T f. Inner FB loop FC slave loop Outer FB loop TC primary loop Explain the reasons for selecting the above configuration, and the disadvantages of dropping each of its three components. 6-24 2
Class Exercise Revisited Continuing the example explored with cascade controllers, suppose the feed flow rate is an important (measured) disturbance, so that the reactor temperature responds as:.5 2s 3 4s T( s) = e TJ ( s) e F( s) 5s + 0s + Design a combined FB cascade and FF control system, and compare its regulatory performance to that of the cascade system alone. Solution: The FF controller is: The previous SIMULINK model is modified and tested. F 6-25 SIMULINK Simulation Model p D (s) Cascade only FF Controller Note where the FF action enters Cascade + FF SIMULINK model to simulate comparison between cascade and cascade + feedforward control 6-26 3
FF Performance Simulation Results Regulatory response of cascade system to a feed rate disturbance. The feed disturbance is sluggishly rejected using only feedback. Regulatory response of cascade controller augmented by feedforward action. In this case, FF action is very efficient! 6-27 Summary On completing this section, you should be able to: Identify processing situations that require special treatment such as cascade, override, auctioneering, feedforward and ratio control, and be able to conceptually design these systems. Correctly design a cascade control system, recognizing that to be effective, the inner loop of a cascade system must be an order of magnitude or more faster than the outer loop. Correctly design a feedforward control system, recognizing that it generally needs to be implemented together with feedback control. 6-28 4