final project_ppt on MIMO System.pptx

8/13/2019 final project_ppt on MIMO System.pptx

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Welcome

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CONTROLLERDESIGNING OF MIMOSYSTEM

(Phase 1)

for the degree of B.Tech.

Instrumentation and Control Engineering

By

Sulagna Sarkar (IC-513)Madhumita Mantri (IC-505)

Pratik Nath (IC-530)

Debayan Sen (IC-526)

Under the Supervision ofMr. Parikshit Kr. Paul

Calcutta Institute of Engineering and Management

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INTRODUCTION

SYSTEMAn inter connection of elements and devices for a desired

purpose.

CONTROL SYSTEMIt is a device or set of device that manages,

commands, directs or regulates the behavior of other device(s) or

system(s).

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Control

System

Output

SignalInput

Signal

Disturbance

Fig 1.diagram of control system


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OPEN LOOP CONTROL SYSTEM:

Without feed back or Non-feedback control system.

control action is independent. output is not compared with the input.

E.g.- Automatic washing machine , Immersion rod.

CLOSED LOOP CONTROL SYTEM:

Known as Feedback Control System.

Control action is dependent on desired output. E.g.- Air conditioner

Fig 2. open loop control system

Fig 3. closed loop control system


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AUTOMATIC CONTROL SYSTEM

A Control System in which regulating and switching operations areperformed automatically in response to predetermined conditions.

Control system automatic control system (Involving machines

only)

E.g.- Design a machine, or use a computer to do it, then the system is an

automatic control system.

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CONTROL SYSTEM CLASSIFICATIONS

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SISO (Single Input

Single Output)

TITO (Two Input TwoOutput)

MIMO(Multiple Input

Multiple Output)

Fig 4. SISO , TITO , MIMO System


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SISO SYSTEM

Single Input Single Output. Single loop control

Control system have only one controlled variable and only one

manipulated variable.

BLOCK DIAGRAM:

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Fig 5. Diagram of SISO system


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TITO SYSTEM

Two Input Two Output System.

It is a type of MIMO system.

Control system have two controlled variable two manipulated

variable.

BLOCK DIAGRAM:

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Fig 6. Diagram of TITO system


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MIMO SYSTEM

Multiple Input Multiple Output.

control systems have more than one controlled variable and more

than one manipulated variable.

BLOCK DIAGRAM:

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Fig 7. Diagram of MIMO system


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APPLICATIONS OF MIMO SYSTEM

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Aircraft Control System

Four Tank System

Fig 8. Aircraft control system

Fig 9. Four tank apparatus


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BLOCK DIAGRAM OF MULTILOOP

CONTROL

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Fig 10. Multiloop control system


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TRANSFER FUNCTION MODEL

Transfer function of a MIMO is very important to determine theeffect of the manipulated variables on the controlled variables.

Two controlled variable two manipulated variable (Four transfer

function required)

InputOutput relation for the process

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In vector matrix,

Where Y(S)= output vector and U(S)= input vector ,written as

=process transfer function matrix, written as

The steady state process transfer matrix (S=0) is called the processgain matrix, K

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CONTROL LOOP INTERACTION

It is a undesirable interaction between two or more control loops.

Control loop interactions are presence due to the third feedback

loop.

Third feedback loop also known as hidden feedback loop

PROBLEM DUE TO HIDDEN FEEDBACK LOOP:

It usually destabilize the whole system.

It makes the controller tuning much more difficult .

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Hidden feedback loop

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Fig 11. 1-1/2-2 pairing control system


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BRISTOLS RELATIVE GAIN ARRAY

METHOD

Bristol(1966) developed a systematic approach for the analysis ofmultivariable process control problems.

It requires only steady state information(the process gain matrix K)

Consider a process with n controlled variable and n manipulated

variables.

The relative gain, relates the ithcontrolled variable and the jthmanipulated variable

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CALCULATION OF RGA

Steady state process model for matrix

The RGA is defined as:

Properties:

1. The sum of the elements in each row or column equal to one

2. The relative gain are dimensionless

3. A large RGA element indicates that small changes in can changethe process control characteristics.

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calculate the value of and expressed as

RGA ,

Where,

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RGA FOR HIGHER ORDER SYSTEM

For higher order matrix, the RGA can be calculated as

Denotes element by element multiplication

= The (i , j) element of K (Steady state gain matrix)

=The (i , j ) element of H

is an element of the transpose of the matrix inverse of K.

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Strategies for Dealing with unwanted control

loop interactions

1. "Detune" one or more FB controllers.

2. Select different manipulated or controlled variables.

e.g., nonlinear functions of original variables

3. Use a decoupling control scheme.4. Use some other type of multivariable control scheme.

Decoupling Control Systems

Basic Idea: Use additional controllers (decoupler) to

compensate for process interactions and thus reduce control

loop interactions

Ideally, decoupling control allows set point changes to affect

only the desired controlled variables.

Typically, decoupling controllers are designed using a simple

process model (e.g., a steady-state model or transfer function


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Block Diagram of Decoupling system


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DecouplerDesign Equations

We want cross-controller, T12, to cancel the effect of U2on Y1.Thus, we would like GP11T12U12+G12U22= 0

or, GP11U12+G12U22= 0

Because U22is not equal to 0 in general, then

T12=-

Similarly, we want T12to cancel the effect of U1on Y2. Thus, werequire that,

GP22T21U11+GP21U11= 0

T21=-

Compare with the design equations for feedforward control based on

block diagram analysis


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Different types of Decoupling

1. Partial Decoupling:

Use only one cross-controller.

2. Static Decoupling:

Design to eliminate Steady-State interactionsIdeal decouplers are merely gains:

T12= -

T21= -

3. Nonlinear Decoupling

Appropriate for nonlinear processes


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CONCLUSION

In this project we have considered control problems with multiple

inputs and multiple outputs using a set of single-loop controllers.

Such MIMO control problems are more difficult than SISO control

problems due to the presence of process interactions. They produce

undesirable control loop interactions for multiloop control. If these

interactions are unacceptable, then different model-based

multivariable control strategies are taken. One such is thedecoupling method which is used to reduce the control loop

interactions.

In MIMO system another problem is that on changing the input

variable output variable also changes. So relative gain array (RGA)

is used for pairing the manipulated and controlled variable to get adesired output.

In this phase we have studied upto this and in our next phase we

want to design a controller on MIMO and implement this on

MATLAB simulink.

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REFERANCE

[1] http://www.google.com

[2] http://www.daenotes.com/electronics/industrial-

electronics/process-control

[3] Benjamin C.Kuo, Automatic Control Systems, 7thEdition

[4] Dale E. Seborg, Thomas F. Edgar, Duncan A. Mellichamp,

Process Dynamics and Control,2ndEdition

[5] N. Jensen, D.G. Fisher, S.L. Shah, Interaction analysis in

multivariable control system, AIChE J. 32 (6) (1986) 959970.

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http://www.daenotes.com/electronics/industrial-http://www.daenotes.com/electronics/industrial-http://www.daenotes.com/electronics/industrial-


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SCOPE OF PROJECT

We want to design controller for MIMO system and to implementthat in MATLAB in our phase 2.

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THANK

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final project_ppt on MIMO System.pptx

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