Introduction to Feedback Control Systems

8/10/2019 Introduction to Feedback Control Systems

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Introduction to Feed

Control Sys


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Introduction

SystemAn interconnection of elements and devices for a desired purpose.

Control SystemAn interconnection of components forming a systemconfiguration that will provide a desired response.

ProcessThe device, plant, or systemunder control. The input and outputrelationship represents the cause-and-effect relationship of the process.


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Introduction

Multivariable Control System

Open-Loop Control Systemsutilize a controller or controlactuator to obtain the desired

response.

Closed-Loop Control Systemsutilizes feedback to comparethe actual output to thedesired output response.


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Feedback Control System

A system whose output is controlled using its measurement as signal

This feedback signal is compared with a reference signal to genesignal which is filtered by a controllerto produce the systems co

Continuous-time linear time-invariant (LTI) feedback systems


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Terminology

Plant is the system to be controlled

Sensor measures the quantity to be controlled

Actuator affects the plant

Controller or control processor processes the sensor signal to dactuator

control law or control algorithm is the algorithm used by the cprocessor to derive the actuator signal


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The controlled system is called the plant, and its LTI model is the tran

P(s).

The disturbed output of the plant is y(t) and its noisy measurement i

corrupted by the measurement noise n(t). The error between the desired output yd(t) and ym(t) is the measured

denoted as em(t)

The actual error between thee plant output and the reference is e(t):


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The output disturbance is the signal do(t) and the output measnoise is n(t).

The feedback measurement sensor dynamics are modelled by G

The actuator (e.g. valve) modelled by Ga(s)is the device that trcontrol signal from the controller K(s) in an action on the plant

The input disturbance di(t) (e.g. friction force) disturbs the confrom the actuator to the plant input


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In many cases, we will assume that the actuator and sensor are

Ga(s)=Gm(s)=1 ), and that measurement noise can be neglected n(t)=0. This will simplify the analysis


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Objectives of feedback control

The main objectives of the feedback control is to ensure that vainterest in a process or a system, thought of as the output signa

Track reference trajectories (called tracking or servo), or

Are maintained close to their set points (called regulation)


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Need for feedback

To counteract disturbance signals affecting the output

To improve system performance in the presence of model unce

to stabilize the unstable plant


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Feedback properties

Robustness to uncertainties

Design of dynamics

Higher levels of automation


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Drawbacks of feedbacks

Possibility for instability if the system is not designed properly

Feedback inherently couples different art of a system

Complexity of embedding a control system into a product


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Simple form of feedback


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e = r y, difference between the reference signal and the outpusystem

The feedback in the equation is called on-off control

Control variable is not defined when the error is zero

Modification: introducing hysteresis or dead zone


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Controllers and

Control Ele


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The concept of a control system is to sense deviation of the out

desired and correct it, till the desired output is achieved.

The deviation of the actual output from the desired value is call

The feedback allows us to compare the actual output with its deto generate the error.

The error is denoted as e(t). The desiredvalue of the output is also called the reference input

point.


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Controller

The controller is an element which accepts the error in some fodecides the proper corrective action.

The output of the controller is then applied to the process or fin

element. This brings the output back to its desired set point va The controller is the heart of a control system.

The controller has its own logic to handle the error.


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Properties of controller


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The actual output is sensed by a sensor and converted to a prosignal b(t) using a feedback element.

The set point value is the reference input r(t).


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ERROR

The error detector compares the feedback signal b(t) with the rinput r(t) to generate the error.

e(t) = r(t) - b(t)

This gives an absolute indication of an error.

Error can also be expressed as the percentage of the measurerange. The range of the measured variable b(t) is also called spa

span= bmaxbmin


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Where e(p) = error as percent of span


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VARIABLE RANGE

In practical systems, the controlled variable has a range of vwhich the control is required to be maintained. This range is spmaximum and minimum values allowed for the controlled variaspecified as some nominal values and plus-minus tolerance a

this value. Such range is important for the design of controllers


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CONTROLLER OUTPUT RANGE

Similar to the controlled variable, a range is associated withoutput variable. It is also specified in terms of the maximum avalues.

But often the controller output is expressed as a perce

minimum controller output is 0% and maximum controller outBut 0% controller output does not mean zero output.


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CONTROL LAG

The control lag is the time required by the process and the cto make the necessary changes to obtain the output at its setpo


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DEAD ZONE

Many times a dead zone is associated with a process control locorresponding to the dead zone is called the dead time. The timbetween the instant when the error occurs and the instant whecorrective action occurs is called the dead time. This part is calle

called dead band.


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Classification of Controllers

The classification of controller is based on the response of the cmode of operation of the controller.

Basically, controllers are classified as discontinuous concontinuous controllers.

The discontinuous mode controllers are further classifiedcontrollers and multiposition controllers.

The continuous mode controllers are further classified as controllers, integral controllers, and derivative controllers. Sommode controllers can be combined to obtain composite contExamples of such composite controllers are PI, PD, and PID con


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Discontinuous Controller Modes

Two controller modes based on the discontinuous changes in the output as the error varies:

Two-Position Mode

Multiposition Mode


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PROPORTIONAL CONTROL MODE

In this control mode, the output of controller is simple propoerror e(t). The relation between the error e(t) and the controlledetermined by constant called proportional gain constant deThe output of the controller is a linear function of the error e(value of the error has a unique value of the controller output. the error which covers 0% to 100% controller output i

proportional band.


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If the controlled variable i.e input to the controller increases, cau

in the controller output, the action is called direct action.

If the controlled variable decreases, causing increase in the contor increase in the controlled variable , causing decrease in toutput , the action is called reverse action.

The proportional band can be mathematically defined by,

PB= 100/Kp


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INTEGRAL CONTROL MODE

In proportional control mode, error reduces but cannot go to zproduces an offset error. When the load changes, the output dthe set point. Such deviation is called offset error. The integratis relatively slow controller. It changes its output at a radependent on the integrating time constant , until the ercancelled. Compared to the proportional control, the inte

requires time to build up an appreciable output. However it contill the error signal disappears. This corrects the problem of thin the proportional controller.


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DERIVATIVE CONTROL MODE

In practice, the error is a function of time and at a particular instzero. But it may not remain zero forever after that instant. action is required corresponding to the rate at which the errorSuch a controller is called derivative controller. In this mode, t

the controller depends on the time rate of change of the Hence it is also called rate action mode or anticipatory action m


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The mathematical equation for the mode is,

p(t)= Kd

d e(t)/ dt

Where Kd = derivative gain constant

The important feature of this type of control mode is that for change of error signal, there is a unique value of the controlle

The advantage of the derivative control action is that it respond

change of error and can produce the significant correctmagnitude of the actuating error becomes too large. Dethus anticipates the actuating error, initiates an early correctends to increase stability of the system improving the transi


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HARDWARES

PROCESS CONT


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What are these hardwares?

the physical, touchable, material parcomputer or other system.

the mechanical equipment necessar

conducting an activity, usually distingufrom the theory and design that makeactivity possible.


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What are these hardwares involved for

control;

Valves

Pressure gauges

Pumps

Part of the Computers

Temperature gauges

Introduction to Feedback Control Systems

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