Adaptive CONTROL UnitIgfh

7/27/2019 Adaptive CONTROL UnitIgfh

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Adaptive control


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Topics covered

What is adaptive control? (Chap 1)

Deterministic self tuning regulators (chap 3)

Model reference adaptive systems (chap 5)

Properties of adaptive systems (chap 6)

Auto tuning (chap 8)

Gain scheduling (chap 9)

Robust and self oscillating systems (chap 10)

Practical issues and implementation (chap 11)


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Introduction

to adapt means to change a behavior to

conform to new circumstances.

An adaptive controller

a controller that can modify its behavior in

response to the changes in dynamics of the

processes and the disturbances acting on the

process.


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Contd..

An adaptive controller

a controller with adjustable parametersand a mechanism for adjusting the

parameters. The parameters are adjusted to compensate

for the changes in dynamics of the plant and

the disturbances acting on the plant. The controller becomes nonlinear because of

the parameter adjustment mechanism


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A block diagram of the adaptive

controller


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Description

An adaptive control system can be thought of

as having two loops.

One loop is a normal feedback with the

process and the controller.

The other loop is the parameter adjustment

loop.

The parameter adjustment loop is usually

slower than the normal feedback loop.


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Circumstances under which adaptive control can be

preferred:

it is convenient to control a plant with theavailable conventional PID controllers.

Some circumstances under which the adaptivecontrollers can perform better than theconventional PID controllers are:

Change in plant transfer function due tovariations in the environment, the size andproperties of the raw materials, wear & tear of

certain components. Stochastic disturbances (disturbances whose

characteristics/behavior are unpredictable )


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Contd..

Change in nature of inputs

Propagation of disturbances along a chain of

unit processes

Nonlinear behavior as in case of complex

chemical or biochemical reaction

Appreciable dead time Unknown parameters, when control system

for new process is commissioned.


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Effects of process variations

The standard approach to control system designis

to develop a linear model for the process for some

operating condition and to design a controller havingconstant parameters.

A fundamental property is also that feedback systemsare intrinsically insensitive to modeling errors anddisturbances.

The mechanisms causing variation in processdynamics and its effect on the performance of controlsystem is studied in the following section.


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Some mechanisms causing variation in

process dynamics are:

Nonlinear actuators

Flow and speed variations

Flight control Variation in disturbance characteristics


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Nonlinear actuators

A very common source of variations is that actuators,

like valves have a nonlinear characteristic.

Let

the static valve characteristics be 0

and let and


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Block diagram of a flow control loop with a PI controller and a

nonlinear valve


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Discussions

Linearizing the system around a steady state

operating point shows that

the incremental gain of the valve is f(u), and

hence the loop gain is proportional to f(u).

The system can perform well at one operating

level and poorly at another


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Step responses for PI control of simple

flow loop at different operating levels


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Discussions

The controller is tuned to give a good

response at low levels of operating level.

For higher values of operating level, the

closed loop system even becomes unstable as

can be seen in fig.3.


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Other examples

Flow and speed variationstank system

Flight Control

Variations in disturbance characteristics arealso discussed for

Ship steering control

Regulation of quality variable in processcontrol


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Adaptive control schemes

Gain scheduling

Model-Reference Adaptive System (MRAS)

Self-Tuning Regulator (STR) Dual Control


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Gain Scheduling

Gain scheduling is an adaptive controlstrategy, where the gain of the system isdetermined and based on its value the

controller parameters are changed. This approach is called gain scheduling

because

the scheme was originally used to measure thegain and then change, that is, schedule thecontroller to compensate for changes in theprocess gain.


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Block diagram of system with gain

scheduling


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Description

The system can be viewed as having two loops.

an inner loop composed of the process and thecontroller

outer loop contains components that adjust thecontroller parameters on the basis of theoperating conditions.

regarded as mapping from process parameters tocontroller parameters.

It can be implemented as a function or a tablelookup.


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Contd..

The concept of gain scheduling originated inconnection with the development of flight controlsystems.

In process control,the production rate-a scheduling variable,

time constants and time delays are inverselyproportional to production rate.

Gain scheduling is a very useful technique forreducing the effects of parameter variations.


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Advantages and disadvantages

Advantages:

Parameters can be changed quickly in response tochanges in plant dynamics

very easy to apply

Drawbacks: It is an open-loop adaptation scheme, with no real

learning or intelligence

The design required for its implementation is

enormous.


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ModelReference Adaptive

System (MRAS)

Used to solve a problem in which the

performance specifications are given in terms

of a reference model.

This model tells how the process output

ideally should respond to the command signal.


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Block diagram of MRAS


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composed of two loops. The inner loop - the process and an ordinary

feedback controller. The outer loop adjusts the controller parameters

in such a way that the error, which is thedifference between the process output yandmodel output ym is small.

The MRAS was originally introduced for flightcontrol.

In this case, the reference model describes thedesired response of the aircraft to joystickmotions.


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The key problem with MRAS is

to determine the adjustment mechanism so that astable system, which brings the error to zero isobtained.

parameter adjustment mechanism, called MIT rule wasused in original MRAS.

e is the error between the plant and model outputs

is the controller parameter.


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The quantity is the sensitivity derivative of

error with respect to the parameter .

The parameter is the adaptation rate.

It is necessary to make approximation to

obtain the sensitivity derivative.

The MIT rule can be regarded as a gradient

scheme to minimize the squared error e2.


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Self Tuning Regulator (STR)

The gain scheduling and MRAS are called

direct methods, because the adjustment rule

tells directly how the controller parameters

should be updated.

A difference scheme is obtained if the

estimates of the process parameters are

updated and the controller parameters areobtained from the solution of a design

problem using the estimated parameters.


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Block Diagram of a STR


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composed of two loops.

The inner loop - the process and an ordinary

feedback controller.

The parameters of the controller are adjusted

by the outer loop, which is composed of a

recursive parameter estimator and a design

calculation.


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It is sometimes not possible to estimate the processparameters without introducing probing controlsignals or perturbations.

The system may be viewed as an automation ofprocess modeling and design, in which the processmodel and the control design are updated at eachsampling period.

A controller of this construction is called a Self TuningRegulator to emphasize that the controllerautomatically tunes its parameters to obtain thedesired properties of the closed loop system.


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Adaptive control problem

An adaptive control problem is formulated by

defining the following:

Description of the process

Possible controller structures and

Adaptation of controller parameters


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Description of the process

The process is usually described by linear Single-input Single-output (SISO)system.

In the continuous time domain, the process is represented in state space as:

Transfer Function form as

Where, s is the Laplace Transform variable.

In discrete time, the process can be described in state space form as:

The discrete time system can also be represented in transfer function form

as: Where, z is the z-transform variable.




Where, s is the Laplace Transform variable.



as: Where, z is the z-transform variable.






as:


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Controller Structures

The process is controlled by a controller

that has adjustable parameters.

Underlying design problem:It is assumed that there exists some

kind of design procedure that makes it

possible to determine a controller thatsatisfies some design criteria, if the

process and its environment are known.


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The adaptive control problem is

used to find a method of adjusting the controller when thecharacteristics of the process and its environment are

unknown or changing. In direct adaptive control, the controller parameters are

changed directly without the characteristics of the processand its disturbance first being determined.

In indirect adaptive methods, the process model and

possibly the disturbance characteristics are firstdetermined.

The controller parameters are designed on the basis of thisinformation.


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Adaptation (adjustment) of controller

parameters

Various techniques are available like

the MIT rule and Lyapunov technique for the

MRAS, MDPP

LQG for STR.

Based on the application and the

performance desired;

any of the techniques can be chosen.


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Construction of an adaptive controller containsthe following steps:

Characterize the behavior of the closed loop

system Determine a suitable control law with

adjustable parameters

Find a mechanism for adjusting theparameters

Implement the control law


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Applications of Adaptive control

aerospace

process control

ship steering

robotics and automotive

biomedical systems.

Adaptive CONTROL UnitIgfh

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