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

Serge Zacher

Bus-Approach for Engineering and Design

• f Feedback Control

IConEST, October 7-10, 2019 in Denver, CO, USA

.

• Dr. Zacher Verlag and University of Applied Sciences Darmstadt, Germany

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First of all I want to thank the ISTES-Organizing Committee for accepting my paper and for good organization

• f virtual presentations!
• Prof. Dr. Serge Zacher

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• Dr. Zacher Verlag and University of Applied Sciences Darmstadt, Germany

• 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

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher

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Content

Introduction ……………………………………… 1. Basics of bus approach ……………………….. 2. Bus approach for simple loops ………………. 2.1 Separate control for many plants …. 2.2 Disturbance compensation ………… 2.3 Cascade control …………………….. 2.4 Redundant Control ……………………

• 3. MIMO: Multi input multi output control …………

3.1 Decoupling control …………………… 3.2 Router …………………………………. Summary ………………………………………… 5 17 23 23 24 25 26 27 27 31 41

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

The feedback control is known since the 17th century. From this time untill now each closed loop consists of a sensor, plant, controller, actuator.

5

Introduction

Steam Weight Lever Spring Wave Sleeve PV (Process Value) Actuator Sensor Lever Controller Plant Steam Boiler SP (Set Point)

• 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).

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Gsensor(s) Gplant(s) Gcontroller(s) Gactuator(s)

Steam Steam Boiler SP (Set Point) PV (Process Value)

• 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.

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Gcontroller(s)

SP Set Point

Gactuator(s) Gsensor(s) Gplant(s)

PV Process Variable     +

This diagram will be usually simplified to only two blocks, the controller GR(s) and the plant Gs(s): GR(s) x(s)



w(s) e(s) y(s) GS(s)

• 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).

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GR(s) x(s)



w(s) e(s) y(s) GS(s)

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

9

Also if many process values x1, x2, x3, x4 should be separately controlled, the classical block diagram is more or less understandable (here is n = 4).

GR1(s)



w1



w2





w3 w4 e1(s) e2(s) e3(s) e4(s) y1(s) x2(s) y2(s) y3(s) y4(s) x1(s) x3(s) x4(s) GR2(s) GS2(s) GS3(s) GR3(s) GR4(s) GS4(s) GS1(s)

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

10

But if the process values are coupled, then the classical block diagram is understandable only for n = 2 variables x1 and x2.

GR1(s) x1 w1 G11(s)

+

G12(s) G21(s) G22(s) GR2(s) w2 e 2 x2

+ + +

GR12(s) GR21(s)

+ +

e 1 y1 y2

+ +

y1R y2R

   

1 2 3 4 1 2 3 GR1(s) x1 w1 G11(s)

+

G12(s) G21(s) G22(s) GR2(s) w2 e 2 x2

+ + +

GR12(s) GR21(s)

+ +

e 1 y1 y2

+ +

y1R y2R

   

1 2 3 4 1 2 3

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

11

The practical use of classical block diagrams with n > 2 coupled variable is difficult, as it is shown in the figure

• n an example with

n = 3 controlled variables x1, x2, x3.

x1 x2 + + + y 1 G23 G32 G31 G22 G11 G12 G21 G13 G33 y 2 y 3 x3 + + + + + + R3 R1 R2 w1 w2 w3    R21 R12 R23 R32 R31 R13 + + + + + + + +       x1 x2 + + + y 1 G23 G23 G32 G32 G31 G31 G22 G22 G11 G11 G12 G12 G21 G21 G13 G13 G33 G33 y 2 y 3 x3 + + + + + + R3 R3 R1 R1 R2 R2 w1 w2 w3    R21 R21 R12 R12 R23 R23 R32 R32 R31 R31 R13 R13 + + + + + + + +      

• 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

• ne variable, but this variable is now a vector with n columns.

The calculation should be done with n x n matrices GR(s) and Gs(s), which is of course very complicated or impossible.

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GR(s) X(s)



W(s) E(s) Y(s) GS(s)

R11 R12 R13 R R21 R22 R23 R31 R32 R33

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) G s G s G s s G s G s G s G s G s G s            G

S

2 5 3 2 1 4 1 6 1 2 4 7 ( ) 5 1 3 1 8 1 4,5 2,5 1 2 1 5 1 1 s s s s s s s s s s                             G

1 2 3

X x x x           

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

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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 Gs(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 GR(s).

So the loop-design by n >2 is possible, but very complicated.

• 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“

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With this expression he described the problem caused by the exponential increase of calculations, which occurs with adding extra dimensions to a mathematical model.

Source: https://en.wikipedia.org/wiki/Richard_E._Bellman

The numerical solution require vastly more computer time when there are more state variables in the model function.

Richard Ernest Bellman

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

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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.

Sensor Sensor Actor

PLC

Point-to-point connection

Field devices Sensor Actor

Sensor Sensor Actor

PLC Field devices Sensor Actor Fieldbus

Server

Bus connection

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

16

The similar solution for feedback control is described in this paper: a virtual bus instead of point-to-point variables connection.

w1 x1(s) e1(s) y1(s)     x1(s) w1 w2 w3 w4 y2(s) x2(s) y3(s) x3(s) y4(s) x4(s) w2 x2(s) e2(s)     w3 x3(s) e3(s)     w4 x4(s) e4(s)     GR1(s) GR2(s) GR3(s) GR4(s) GS1(s) GS2(s) GS3(s) GS4(s)

Bus connection Point-to-point connection

In the literature the feedback control is shown like closed loop.

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• 1. Basics of Bus-Approach
• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher

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) y(s) x(s) GR(s) x(s)



w(s) e(s) y(s) GS(s)

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

x(s) y(s) x(s) Let us put the same blocks from block diagram in the bus below: the plant, the controller and the addition.

 +

w(s) e(s)

GR(s) x(s)



w(s) e(s) y(s) GS(s) GR(s) GS(s)

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

Finally we connect the two x(s)-busses together to get a

• feedback. Now we have two different views of the same loop:

classical way above and bus approach below.

w(s)

x(s) y(s) x(s)

 +

w(s) e(s)

GR(s) x(s)



w(s) e(s) y(s) GS(s) GR(s) GS(s)

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The transfer functions of the bus-system are the same as of the classical closed loop.

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher

GR (s) x(s) w(s) e(s)



GS(s) y(s)

+

x(s) Gvw(s) z(s)

+

G0(s) Gvz(s)

+

GR (s) x(s) w(s) e(s)



GS(s) y(s)

+

x(s) Gvw(s) z(s)

+

G0(s) Gvz(s)

+

vw R S

( ) ( ) ( ) G s G s G s 

Forwards transfer function for reference behaviour

vz S

( ) ( ) G s G s 

Forwards transfer function for disturbance behaviour

R S

( ) ( ) ( ) G s G s G s 

Open loop transfer function

vz z

( ) ( ) 1 ( ) G s G s G s  

Closed loop transfer function for disturbance behaviour

) ( 1 ) ( ) (

vw w

s G s G s G  

Closed loop transfer function for reference behaviour

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Question 1: Is it possible to realize the closed loops with real busses like PROFIBUS?

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher

Answer: The answer is “yes” and “no”. “Yes”, if we have to connect the real hardware. “No”, if we have to analyse the loop, handling with the transfer functions and not with the real hardware. In other words, the bus approach, presented here, is about a virtual bus as a tool for the graphical block diagrams. Question 2: Can we simulate the bus approach with MATLAB/Simulink? Answer: Yes, we can. With the Simulink-Library elements Bus-Creator and Bus Selector.

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher

Bus creator Bus selector Bus creator Bus selector

The MATLAB/Simulink-model of a simple loop with bus- creator and bus-selector.

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

• 2. Bus-Approach for simple loops

1th plant 2nd plant 1th controller 2nd controller

w1 x1 w2 x2

2.1 Separate control for many plants

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Two P-T2-plants, each plant controlled with its PI-controller.

set point w1 set point w2

2.2 Disturbance compensation

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

The compensator GRz(s) is calculated so, that after a step

• f disturbance z = 2 by t =30 s the condition x(s) = 0 will

be fulfilled and the disturbance disappeared.

compensator GRz(s)

w x

disturbance z set point w

2.3 Cascade control

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

The main controller has the set point is w and controlled x(s). The internal controller is for variable x1(s). The set point of the internal controller w1 is the output of the main controller.

internal controller main controller set point w1 set point w

2.4 Redundant control

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

main controller redundant controller

If a disturbance occurs, the “safe” and “control” variables will differ one from another. The redundant switch (not shown below) will connect the redundant controller instead of main controller.

control variable safe variable disturbance set point

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• 3. Multi input multi output control
• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

3.1 Decoupling MIMO-Control

Without bus approach

The use of bus approach has many advantages by application for systems with many plants, many controllers and many controlled variables. In the figure in shown the classical block diagram of the plant, which n = 3 variables are coupled together. It is difficult to follow the signal ways and to decouple the control.

x1 x2 + + + y 1 G23 G32 G31 G22 G11 G12 G21 G13 G33 y 2 y 3 x3 + + + + + + R3 R1 R2 w1 w2 w3    R21 R12 R23 R32 R31 R13 + + + + + + + +       x1 x2 + + + y 1 G23 G23 G32 G32 G31 G31 G22 G22 G11 G11 G12 G12 G21 G21 G13 G13 G33 G33 y 2 y 3 x3 + + + + + + R3 R3 R1 R1 R2 R2 w1 w2 w3    R21 R21 R12 R12 R23 R23 R32 R32 R31 R31 R13 R13 + + + + + + + +      

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

x1 x2 + + + y 1 G23 G32 G31 G22 G11 G12 G21 G13 G33 y 2 y 3 x3 + + + + + + R3 R1 R2 w1 w2 w3    R21 R12 R23 R32 R31 R13 + + + + + + + +       x1 x2 + + + y 1 G23 G23 G32 G32 G31 G31 G22 G22 G11 G11 G12 G12 G21 G21 G13 G13 G33 G33 y 2 y 3 x3 + + + + + + R3 R3 R1 R1 R2 R2 w1 w2 w3    R21 R21 R12 R12 R23 R23 R32 R32 R31 R31 R13 R13 + + + + + + + +      

Instead of the classical block diagram the bus approach allows to follow the signal ways and to design the decoupling.

x1 x1 y3

1

5

3 2 4

w1 x2

 +

R12 R1 e1 y1y2 G11 a12 x2 w2

+ +   +

R2 e2 G22 a21

 + + +

R21

 +

R3 e3 G33 a31

+ +

R31 w3 x3 x3 R13 a13

+

R23 a23

+

R32 a32

+  +   +  6 7 8 + + +

x1 x1 y3

1

5

3 2 4

w1 x2

 +

R12 R1 e1 y1y2 G11 a12 x2 w2

+ +   +

R2 e2 G22 a21

 + + +

R21

 +

R3 e3 G33 a31

+ +

R31 w3 x3 x3 R13 a13

+

R23 a23

+

R32 a32

+  +   +  6 7 8 + + +

With bus approach Without bus approach

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

MIMO-control with bus approach and without decoupling.

Bus creator Bus selector Bus creator Bus selector

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

MIMO-control with bus approach and with decoupling.

For n = 2 are needed N = 4 decoupled controllers For n = 3 like here are needed N = 6 decoupled controllers For n = 4 are needed N = 12 decoupled controllers

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

3.2 Router instead of decoupled control Router is new element, proposed in my books, which is build on another principle as classical decoupled

• controller. The router gets its inputs

from each main controller.

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

MIMO control with n = 4 variables has 4 routers. Instead of it the classical system would had 12 Blocks.

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Question 3: Do you have some practical application of bus approach?

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher

Answer: Yes, I do. One of them is a three tank system. All tanks are connected together and each tank has his own set point w1, w2 , w3. The process values are the levels of each tank x1, x2, x3.

Pumpe 1 Pumpe 2 Tank 1 Tank 3

V1 V3 V2 V13 V32

Tank 2

x1 x2 x3

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher

Answer: Yes, MATLAB/Simulink model with bus approach for MIMO-control

• f the three tank system with n = 3 variables x1, x2, x3.

x1 x2 x3 x1 x2 x3 w1 w2 w3

35

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher

The trend window of the three tank system control with n = 3 with bus approach simulated with MATLAB/Simulink.

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher

The three tank system control with n = 3 variables implemented with PLC Freelance of ABB.

x1 x2 x3

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• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher

The trend window of the three tank system control with n = 3 variables with PLC Freelance of ABB.

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Question 4: The MIMO control will be usually designed with state space control methods. Which advantages has the bus approach against state space methods?

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher

Answer: Well, by using of state space methods we should first transform the transfer functions into state space model. Then we should check the controllability and observability. This steps are not needed by bus approach. The tuning of feedback may be done by state space with pole placing method. But after that the state space controller should be expanded with integrated part. This step also will be omitted by bus approach.

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Question 5: Ok, you said, that bus approach brings no advantages for the engineering of single loops with only one controlled variable. But what advantages has the engineering of MIMO control except of decoupling and dimensionality reducing?

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher

Answer: Well, alone the dimensionality reducing is a great advantage. But except of this the bus approach lets:

• avoid undesirable D-parts (differential terms) by control
• accelerate decoupling MIMO-control
• apply Smith-Predictors into control

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Question 7: Where can I read more about bus approach?

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control University of Applied Sciences Darmstadt and Verlag.Dr. Zacher

Answer: In my books:

• Bus-Approach for Feedback MIMO-Control,

Verlag Dr. Zacher, 2014, Wiesbaden, ISBN 978-3-037638-24-9

• Regelungstechnik für Ingenieure,

Springer Vieweg Verlag, 15. Auflage, 2017, Wiesbaden, ISBN 978-3-658-17631-0

• https://www.szacher.de/my-Books/Bus/

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Summary

• Prof. Dr. Serge Zacher (Stuttgart, Germany)

Bus-Approach for Engineering and Design of Feedback Control www.zacher-automation.de

The bus approach:

• is simplier, not as voluminous as the state space method,
• is easy to implement to the systems of higher order,
• lets to decouple the MIMO control only following the signal

ways on the block diagram or using new element router.

• Prof. Dr. Serge Zacher, 2019

I am sure that you will be surprised, how easy is to handle the feedback control systems of higher order with the bus- approach. Thank you for attention! Please let me know if you have any questions or comments: info@szacher.de

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Bus-Approach for Engineering and Design

• f Feedback Control

October 7-10, 2019, Denver, CO, USA .

END

• f virtual presentation
• Dr. Zacher Verlag and University of Applied Sciences Darmstadt, Germany

Serge Zacher