757
CHAPTER 18
CONTROL SYSTEM DESIGN
USING STATE-SPACE METHODS
Krishnaswamy Srinivasan
Department of Mechanical Engineering
The Ohio State University
Columbus, Ohio
1
INTRODUCTION
757
2 THE POLE PLACEMENT
DESIGN METHOD
758
2.1 Regulation Problem
758
2.2 Modification for Constant
Reference and Disturbance
Inputs
761
3 THE STANDARD LINEAR
QUADRATIC REGULATOR
PROBLEM
762
3.1 The Continuous-Time LQR
Problem
763
3.2 The Discrete-Time LQR
Problem
764
3.3 Stability and Robustness
of the Optimal-Control Law
766
4 EXTENSIONS OF THE LINEAR
QUADRATIC REGULATOR
PROBLEM
768
4.1 Disturbance Accommodation
768
4.2 Tracking Applications
770
4.3 Frequency Shaping of Cost
Functionals
772
4.4 Robust Servomechanism
Control
774
5 DESIGN OF LINEAR STATE
ESTIMATORS
776
5.1 The Observer
777
5.2 The Optimal Observer
781
6 OBSERVER-BASED
CONTROLLERS
783
7 CONCLUSION
788
REFERENCES
788
1
INTRODUCTION
The advantages of feedback control in achieving desired input /output relationships are well
known. Control system theory based on a frequency-domain approach1 illustrates clearly that
the following aspects of single-input–single-output (SISO) system performance can be im-
proved by feedback: (1) the ability to follow reference inputs accurately in the steady state
or under transient conditions and (2) the ability to reject disturbance inputs and reduce
sensitivity of the overall controlled system behavior to plant parameter variations and mod-
eling errors. For multiple-input–multiple-output (MIMO) systems, the coupling between
individual inputs and outputs can be modified in a desired manner, in addition to the per-
formance features already mentioned, by appropriate control system design.2
State-space methods for control system design result in solutions that utilize the state
of the system most effectively for feedback. The resulting state-variable feedback control
systems improve the same aspects of system performance as previously mentioned. However,
the available state-space design procedures accommodate some performance specifications
m