EES42042 - Fundamental of Control Systems Controller...

EES42042 - Fundamental of Control Systems

Controller Design via Controller Design via Root LocusRoot Locus

The Industrial Operations HierarchyThe Industrial Operations Hierarchy

Supervision Supervision

Control Control

Process 1 Process 2

Management, Coordination,Optimization

• Estimator management• Controller management• Fault detection• Fault diagnose• Fault isolation

• Adjustment mechanism• Control algorithm: PA,

MPC, deadbeat, MV, Fuzzy, NN, Ackermann

Analysis and Control ObjectivesAnalysis and Control Objectives

Improving steady state errorImproving transient responseStabilityLow costRobustness

Table 9.7 Types of cascade compensators (continued on next slide)

Table 9.7 Types of cascade compensators (continued)

The Relay ExperimentThe Relay ExperimentAutotuningAutotuning PID ControllerPID Controller

Process

Disturbancee(t)PID Control

Signal Proc. Unit

PID Control Rule-Base

Relay Block

Referencesignal

Controlsignalu(t)

Outputsignaly(t)

SelfSelf--Tuning Control System SchemeTuning Control System Scheme((22--DOF ControllerDOF Controller))

Controlsignal

Outputsignaly(t)

G(z-1)F(z-1)

Referencesignal

w(t) H(z-1)G(z-1)

Recursiveestimator

Controllersynthesis

Configurationrequirements

Performancerequirements Estimated system

parameters; A, B

Controllerparameters; H, F, G

2-DOF controller

Pressure process rig

Adjustment mechanism

PRBSGenerator

Pole assignment

Deadbeat

Figure 9.1a. Sample root locus,showing possibledesign point viagain adjustment (A)and desired designpoint that cannot bemet via simple gainadjustment (B);b. responses frompoles at A and B

IntroductionIntroduction

Figure 9.2Compensationtechniques:a. cascade;b. feedback

Figure 9.3Pole at A is:a. on the rootlocus without compensator;b. not on theroot locus withcompensatorpole added;(figure continues)

Improving Steady State ErrorImproving Steady State Error

Figure 9.3(continued)c. approximately on the root locus with compensator pole and zero added

Figure 9.4Closed-loopsystem forExample 9.1:a. beforecompensation;b. after ideal integralcompensation

Figure 9.5Root locus foruncompensatedsystem ofFigure 9.4(a)

Figure 9.6Root locus forcompensatedsystem of Figure 9.4(b)

Figure 9.7Ideal integral compensated system response and theuncompensated system response of Example 9.1

Figure 9.8PI controller

Figure 9.9a. Type 1 uncompensated system;b. Type 1 compensatedsystem;c. compensatorpole-zero plot

Lag CompensationLag Compensation

Figure 9.10Root locus:a. before lag compensation;b. after lag compensation

Figure 9.11Compensated systemfor Example 9.2

Figure 9.12Root locus forcompensated system of Figure 9.11

Table 9.1Predicted characteristics of uncompensated and lag-compensated systems for Example 9.2

Figure 9.13Step responses ofuncompensated andlag-compensatedsystems forExample 9.2

Figure 9.14Step responses of the system for Example 9.2 using different lag compensators

Figure 9.15Using ideal derivative compensation:a. uncompensated; b. compensator zero at –2;

Improving Transient ResponseImproving Transient Response

Figure 9.15 (continued)c. compensator zero at –3; d. compensator zero at – 4

Figure 9.16Uncompensated system and ideal derivativecompensation solutions from Table 9.2

Table 9.2Predicted characteristics for the systems of Figure 9.15

Figure 9.17Feedbackcontrol systemfor Example 9.3

Figure 9.18Root locus for uncompensatedsystem shown in Figure 9.17

Table 9.3Uncompensated and compensated system characteristics for Example 9.3

Figure 9.19Compensateddominant polesuperimposed over the uncompensatedroot locus forExample 9.3

Figure 9.20Evaluating the location of the compensatingzero for Example 9.3

Figure 9.21Root locus for thecompensated system of Example 9.3

Figure 9.22Uncompensated andcompensated system step responses ofExample 9.3

Figure 9.23PD controller

Figure 9.24Geometry of leadcompensation

Lead CompensationLead Compensation

Figure 9.25Three of the infinitepossible leadcompensator solutions

Figure 9.26Lead compensatordesign, showingevaluation ofuncompensatedand compensateddominant poles forExample 9.4

Table 9.4 Comparison of lead compensation designs for Example 9.4

Figure 9.27s-plane pictureused to calculatethe location ofthe compensator pole for Example 9.4

Figure 9.28Compensated systemroot locus

Figure 9.29Uncompensatedsystem and leadcompensationresponses forExample 9.4

Figure 9.30PID controller

PID Controller DesignPID Controller Design

Figure 9.31Uncompensated feedback control system for Example 9.5

Figure 9.32Root locus for theuncompensatedsystem ofExample 9.5

Table 9.5Predicted characteristics of uncompensated, PD- , and PID-compensated systems of Example 9.5

Figure 9.33Calculating thePD compensator zero for Example 9.5

Figure 9.34Root locus forPD-compensatedsystem ofExample 9.5

Figure 9.35Step responses foruncompensated,PD-compensated, andPID-compensatedsystems ofExample 9.5

Figure 9.36Root locus for PID-compensatedsystemof Example 9.5

Figure 9.37Uncompensatedsystem forExample 9.6

LagLag--lead Compensator Designlead Compensator Design

Figure 9.38Root locus for uncompensatedsystem of Example 9.6

Table 9.6Predicted characteristics of uncompensated, lead-compensated, and lag-lead- compensated systems of Example 9.6

Figure 9.39Evaluating thecompensator pole forExample 9.6

Figure 9.40Root locus for lead-compensated system of Example 9.6

Figure 9.41Root locus for lag-lead-compensated systemof Example 9.6

Figure 9.42Improvement in step response forlag-lead-compensatedsystem ofExample 9.6

Figure 9.43Improvement inramp response error for the system ofExample 9.6:a. lead-compensated;b. lag-lead-compensated

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