Feedback Control system

Advantages of Feedback in ControlCompared to open-loop control, feedback canbe used to:

• Reduce the sensitivity of a system’stransfer function to parameter changes

• Reduce steady-state error in responseto disturbances,

• Reduce steady-state error in tracking areference response (& speed up thetransient response)

• Stabilize an unstable process

Disadvantages of Feedback in Control

Compared to open-loop control,

• Feedback requires a sensor that can be veryexpensive and may introduce additionalnoise

• Feedback systems are often more difficult todesign and operate than open-loop systems

• Feedback changes the dynamic response(faster) but often makes the system lessstable.

Control system

Controlled system

Control Modes• There are a number of ways by which a control unit can

be react to an error signal and supply an output forcorrecting elements:

• 1- two step mode: the controller is an ON-OFF correctingsignal

• 2- The proportional Mode: the controller produce acontrol action proportional to the error.

• 3: the derivative mode D: the controller produces acontrol action proportional to the rate at which the error ischanging. When there is a sudden change in the errorsignal, the controller gives alarge correcting signal, whenthere is a gradual change only a small correcting signal isproduces. Normally used in conjunction with proportionalcontrol

Control Modes

• 4- The integral mode: the control actionproportional to the integral of the error thus aconstant error signal e=constant produces anincreasing correcting signal

• 5- Combination of Modes PD, PI, PID

• A controller can achieve these modes by meansof pneumatic circuit, analogue electronic circuitsinvolving opamp or by the programming of amicroprocessor or computer system

Two-step control

Two step modeAn example of two step mode of control is the bimetallicthermostat that might be used with a simple temperaturecontrol system.

• Consequences:

• To avoid continuousswitching ON and OFF onrespond to slight change,two values are normallyused, a dead band is usedfor the values between theON and OFF values

• Large dead band implieslarge temp. fluctuations

• Small dead band increaseswitching frequency

Two step mode

Bolton, Mechatronics PowerPoints, 4th Edition, © Pearson Education Limited 2008

Two step mode•The bimetallicelement haspermanent magnet fora switch contact, thishas the effect ofproducing a deadband.Fast ON-OFF controlcan be used for motorcontrol usingcontrolled switchingelements (MOSFET,

Thyrester)

Proportional Mode• With the two step method of control, the

controller output is either ON or OFF signal,regardless of the magnitude of error.

• With proportional control mode, the size of thecontroller output is proportional to the size of theerror. The bigger the error the bigger the outputfrom the controller

• Controller output u(t) = Kp e

• Or in s domain U(s)=KpE(s)

Proportional controller

Electronic Proportional ModeA summing opamp with an inverter can be used asproportional controller

Electronic Proportional Mode

Proportional controller for temperature control

Electronic Proportional Mode

System response to proportional control

Derivative control mode

As soon as the error signalbegins to change, there can bequite a large controller output,thus rapid initial response toerror signal occur

In Figure the controller outputis constant is constantbecause the rate of change isconstant.

• - They do not response to steady- state errorsignal, that is why always combined with P-controller

• P responds to all error• D responds to rate of change

• Derivative action can also be a problem if themeasurement of the process variable gives anoisy signal, the rapid fluctuations of thenoise resulting in outputs which will be seenby the controller as rapid changes in errorand so give rise to significant outputs fromthe controller.

Derivative control mode

Derivative controller

Derivative control mode

The Figure shows the form of an electronic derivativecontroller circuit, it composed of two operationalamplifier: integrator + Inverter

PD controller

PD controller

due to the derivativefollowed by the gradualchange due toproportional action.

This form of control thusdeal with fast processchanges

Integral control

Integral control

Integral control

Figure shows the action of anintegral controller when there isa constant error input to thecontroller

When the controller output isconstant, the error is zero;when controller output is variesat a constant rate, the error hasa constant value.

Electronic Integral controller

Integral controlThe integrator is connected to the error signal at time t, whilethe second integrator is connected to the error at t=0- i.e. (t-Ts)

PI control

PI control

PID Controller

PID circuit

Risetime Maximumovershoot

Settlingtime

Steady-stateerror

P Decrease Increase Smallchange

Decrease

I Decrease Increase Increase Eliminate

D Smallchange

Decrease Decrease Smallchange

PID & Closed-loop Response

• Note that these correlations may not be exactly accurate, because P, I and D gains are dependent of each other.

PID Response

PDP

PI PID

PID Conclusions• Increasing the proportional feedback gainreduces steady-state errors, but high gainsalmost always destabilize the system.

• Integral control provides robust reduction insteady-state errors, but often makes thesystem less stable.

• Derivative control usually increasesdamping and improves stability, but hasalmost no effect on the steady state error

• These 3 kinds of control combined from theclassical PID controller

Digital closed-loop control system

A digital controller basically operates through the following cycle

1- samples the measured value

2- compares it with the set value and establishes the error

3- carries out calculation based on the error value and store valuesof previous inputs and outputs to obtain the output signal

4- sends the output signal to the DAC.

5- Waits until the next samples time before repeating the cycle.

Digital PID Controller

System with velocity feedback: (a) descriptive diagram of the system,(b) block diagram of the system

Self-tuning

Model-referenced control