Bus-Approach for Engineering and Design of Feedback Control . - PowerPoint PPT Presentation

Serge Zacher Bus-Approach for Engineering and Design of Feedback Control . IConEST, October 7-10, 2019 in Denver, CO, USA Dr. Zacher Verlag and University of Applied Sciences Darmstadt, Germany 1

First of all I want to thank the ISTES-Organizing Committee for accepting my paper and for good organization of virtual presentations! Prof. Dr. Serge Zacher Dr. Zacher Verlag and University of Applied Sciences Darmstadt, Germany 2

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de Then I want shortly introduce myself: 1962 – Dipl.-Ing. ( Diplom-Engineer of Automation ) 1967 – Dr.-Ing. ( Doctor of Engineering ) 1984 – Dr. sc. techn. ( Doctor of technical sciences ) 1991 – Professor of various Universities of Applied Sciences 3

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher Content 5 Introduction ……………………………………… 17 1. Basics of bus approach ……………………….. 23 2. Bus approach for simple loops ………………. 23 2.1 Separate control for many plants …. 24 2.2 Disturbance compensation ………… 25 2.3 Cascade control …………………….. 26 2.4 Redundant Control …………………… 27 3. MIMO: Multi input multi output control ………… 27 3.1 Decoupling control …………………… 31 3.2 Router …………………………………. Summary ………………………………………… 41 4

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de Introduction The feedback control is known since the 17th century. From this time untill now each closed loop consists of a sensor, plant, controller, actuator. Lever Spring Sensor Weight Controller Lever Sleeve Actuator SP (Set Point) Wave Steam Plant Steam Boiler PV (Process Value) 5

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de Each element of the loop is mathematically described as a transfer function G ( s ). G sensor ( s ) G controller ( s ) G actuator ( s ) SP (Set Point) Steam Steam Boiler G plant ( s ) PV (Process Value) 6

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de The classical block-diagram of a closed loop is shown below. PV SP Process Set Point Variable G actuator ( s ) G plant ( s ) G controller ( s ) +     G sensor ( s ) This diagram will be usually simplified to only two blocks, the controller G R ( s ) and the plant Gs ( s ) : w ( s ) e ( s ) x ( s ) y ( s ) G S ( s ) G R ( s )  7

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de The аnalysis and the design of such loops with only one controlled variable x ( s ) are well known. It belongs to the basics of all technical universities courses. The control theory is well developed and is widely implemented in the praxis. So there is no need to suggest a new approach for such loops with only one controlled variable ( n =1). w ( s ) e ( s ) x ( s ) y ( s ) G S ( s ) G R ( s )  8

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de Also if many process values x 1 , x 2 , x 3 , x 4 should be separately controlled, the classical block diagram is more or less understandable (here is n = 4). y 1 ( s ) x 1 ( s ) w 1 e 1 ( s ) G R1 ( s ) G S1 ( s )  y 2 ( s ) e 2 ( s ) x 2 ( s ) w 2 G R2 ( s ) G S2 ( s )  x 3 ( s ) e 3 ( s ) y 3 ( s ) w 3 G S3 ( s ) G R3 ( s )  x 4 ( s ) y 4 ( s ) e 4 ( s ) w 4 G R4 ( s ) G S4 ( s )  9

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de But if the process values are coupled, then the classical block diagram is understandable only for n = 2 variables x 1 and x 2 .   y 1 y 1 e 1 e 1 w 1 w 1 x 1 x 1 + + + + G R1 ( s ) G R1 ( s ) G 11 ( s ) G 11 ( s ) y 1R y 1R 1 1 1 1 + +   + + G R12 ( s ) G R12 ( s ) G 12 ( s ) G 12 ( s ) 3 3 G R21 ( s ) G R21 ( s ) G 21 ( s ) G 21 ( s ) 3 3 2 2 2 2   + + y 2R y 2R x 2 x 2 y 2 y 2 w 2 w 2 e 2 e 2 + + G R2 ( s ) G R2 ( s ) G 22 ( s ) G 22 ( s ) + + + + 4 4   10

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de   y 1 y 1 x 1 x 1 w 1 w 1 The practical use of + + + + + + G 11 G 11 G 11 R 1 R 1 R 1 + + + +     + + classical block G 12 G 12 G 12 R 12 R 12 R 12 diagrams with n > 2 R 21 R 21 R 21 G 21 G 21 G 21 coupled variable is R 13 R 13 R 13 G 13 G 13 G 13 R 31 R 31 R 31 G 31 G 31 G 31 difficult, as it is   + + w 2 w 2 y 2 y 2 x 2 x 2 + + + + R 2 R 2 R 2 G 22 G 22 G 22 shown in the figure + +     + + R 23 R 23 R 23 G 23 G 23 G 23 on an example with R 32 R 32 R 32 G 32 G 32 G 32 n = 3 controlled   + + + + x 3 x 3   y 3 y 3 w 3 w 3 G 33 G 33 G 33 R 3 R 3 R 3 + + variables x 1 , x 2 , x 3 . + + + + + +   11

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de To solve this problem the block diagram will be shown with only one variable, but this variable is now a vector with n columns. The calculation should be done with n x n matrices G R ( s ) and G s ( s ), which is of course very complicated or impossible .   2 5 3    x     2 s 1 4 s 1 6 s 1  G ( ) s G ( ) s G ( ) s    1   R11 R12 R13       2 4 7 X x    G ( ) s G ( ) s G ( ) s G ( ) s   G ( ) s  2  S R R21 R22 R23      5 s 1 3 s 1 8 s 1     x   G ( ) s G ( ) s G ( ) s     3 4,5 2,5 1 R31 R32 R33      2 s 1 5 s 1 s 1   X( s ) W( s ) E( s ) Y( s ) G S ( s ) G R ( s )  12

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de The only one known solution for this case, namely if n > 2, is the state space control . According to the state space control the transfer function of a plant G s( s ) will be transfered into numerical matrices A, B, C and D. The so called P-canonical model or V-canonical model of the closed loop will be build. The design of the loop will be done in many steps. First we check the observability and the controllability of the canonican model. Is the A , B , C , D -model not controllable, no controller design with the state space control is possible. Supposing the model was controllable we complete the A , B , C , D -model with some controller with an integrated part, e.g. I-, PI- or PID-controller, and define its parameters. And finally we will implement the results of A , B , C , D - model on the loop with the real controller G R ( s ). So the loop-design by n >2 is possible, but very complicated. 13

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de Richard Bellman called such problems „Curse of Dimensionality“ With this expression he described the problem caused by the exponential increase of calculations, which occurs with adding extra dimensions to a mathematical model. The numerical solution require vastly more computer time when there are more state variables in the model function. Source: https://en.wikipedia.org/wiki/Richard_E._Bellman Richard Ernest Bellman 14

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de In the information technology the solution for the „Curse of dimensionality“ is well known, namely: instead of point-to-point connection we use a bus. Bus connection Point-to-point connection PLC PLC Fieldbus Server Sensor Sensor Sensor Sensor Actor Sensor Sensor Actor Actor Actor 15 Field devices Field devices

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de The similar solution for feedback control is described in this paper: a virtual bus instead of point-to-point variables connection. Bus connection Point-to-point connection y 1 ( s ) x 1 ( s ) G S1 ( s ) e 1 ( s ) w 1 G R1 ( s ) y 2 ( s ) x 2 ( s ) x 1 ( s )     G S2 ( s ) w 2 e 2 ( s ) G R2 ( s ) y 3 ( s ) x 3 ( s ) G S3 ( s ) x 2 ( s )     w 3 e 3 ( s ) y 4 ( s ) x 4 ( s ) G R3 ( s ) G S4 ( s ) x 3 ( s )     e 4 ( s ) w 4 w 1 G R4 ( s ) x 4 ( s )     w 2 w 3 w 4 16

Prof. Dr. Serge Zacher (Stuttgart, Germany) Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher 1. Basics of Bus-Approach In the literature the feedback control is shown like closed loop. x ( s ) w ( s ) e ( s ) y ( s ) G R ( s ) G S ( s )  Now let us apply instead of closed loop a virtual bus, which consists of two busses, one for x ( s ) and another for y ( s ) . x ( s ) x ( s ) y ( s ) 17