EES42042 - Fundamental of Control Systems Controller...
Transcript of 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
Low
laye
rH
igh
laye
rP
roce
ss
• 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
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Table 9.7 Types of cascade compensators (continued on next slide)
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Table 9.7 Types of cascade compensators (continued)
The Relay ExperimentThe Relay ExperimentAutotuningAutotuning PID ControllerPID Controller
-
Process
Disturbancee(t)PID Control
Law
Signal Proc. Unit
PID Control Rule-Base
Relay Block
Referencesignal
w(t)
Controlsignalu(t)
Outputsignaly(t)
SelfSelf--Tuning Control System SchemeTuning Control System Scheme((22--DOF ControllerDOF Controller))
Controlsignal
u(t)
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
RLS
RIV
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
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
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
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.3(continued)c. approximately on the root locus with compensator pole and zero added
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.4Closed-loopsystem forExample 9.1:a. beforecompensation;b. after ideal integralcompensation
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.5Root locus foruncompensatedsystem ofFigure 9.4(a)
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.6Root locus forcompensatedsystem of Figure 9.4(b)
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.7Ideal integral compensated system response and theuncompensated system response of Example 9.1
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.8PI controller
Figure 9.9a. Type 1 uncompensated system;b. Type 1 compensatedsystem;c. compensatorpole-zero plot
Lag CompensationLag Compensation
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.10Root locus:a. before lag compensation;b. after lag compensation
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.11Compensated systemfor Example 9.2
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.12Root locus forcompensated system of Figure 9.11
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Table 9.1Predicted characteristics of uncompensated and lag-compensated systems for Example 9.2
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.13Step responses ofuncompensated andlag-compensatedsystems forExample 9.2
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
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
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.15 (continued)c. compensator zero at –3; d. compensator zero at – 4
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.16Uncompensated system and ideal derivativecompensation solutions from Table 9.2
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Table 9.2Predicted characteristics for the systems of Figure 9.15
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.17Feedbackcontrol systemfor Example 9.3
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.18Root locus for uncompensatedsystem shown in Figure 9.17
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Table 9.3Uncompensated and compensated system characteristics for Example 9.3
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.19Compensateddominant polesuperimposed over the uncompensatedroot locus forExample 9.3
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.20Evaluating the location of the compensatingzero for Example 9.3
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.21Root locus for thecompensated system of Example 9.3
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.22Uncompensated andcompensated system step responses ofExample 9.3
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.23PD controller
Figure 9.24Geometry of leadcompensation
Lead CompensationLead Compensation
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.25Three of the infinitepossible leadcompensator solutions
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.26Lead compensatordesign, showingevaluation ofuncompensatedand compensateddominant poles forExample 9.4
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Table 9.4 Comparison of lead compensation designs for Example 9.4
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.27s-plane pictureused to calculatethe location ofthe compensator pole for Example 9.4
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.28Compensated systemroot locus
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.29Uncompensatedsystem and leadcompensationresponses forExample 9.4
Figure 9.30PID controller
PID Controller DesignPID Controller Design
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.31Uncompensated feedback control system for Example 9.5
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.32Root locus for theuncompensatedsystem ofExample 9.5
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Table 9.5Predicted characteristics of uncompensated, PD- , and PID-compensated systems of Example 9.5
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.33Calculating thePD compensator zero for Example 9.5
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.34Root locus forPD-compensatedsystem ofExample 9.5
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.35Step responses foruncompensated,PD-compensated, andPID-compensatedsystems ofExample 9.5
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.36Root locus for PID-compensatedsystemof Example 9.5
Figure 9.37Uncompensatedsystem forExample 9.6
LagLag--lead Compensator Designlead Compensator Design
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.38Root locus for uncompensatedsystem of Example 9.6
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Table 9.6Predicted characteristics of uncompensated, lead-compensated, and lag-lead- compensated systems of Example 9.6
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.39Evaluating thecompensator pole forExample 9.6
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.40Root locus for lead-compensated system of Example 9.6
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.41Root locus for lag-lead-compensated systemof Example 9.6
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.42Improvement in step response forlag-lead-compensatedsystem ofExample 9.6
Control Systems Engineering, Fourth Edition by Norman S. NiseCopyright © 2004 by John Wiley & Sons. All rights reserved.
Figure 9.43Improvement inramp response error for the system ofExample 9.6:a. lead-compensated;b. lag-lead-compensated