Page 187 - Modern Control Systems
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CHAPTER
3 State Variable Models
3.1 Introduction 162
3.2 The State Variables of a Dynamic System 162
3.3 The State Differential Equation 166
3.4 Signal-Flow Graph and Block Diagram Models 171
3.5 Alternative Signal-Flow Graph and Block Diagram Models 182
3.6 The Transfer Function from the State Equation 187
3.7 The Time Response and the State Transition Matrix 189
3.8 Design Examples 193
3.9 Analysis of State Variable Models Using Control Design Software 206
3.10 Sequential Design Example: Disk Drive Read System 209
3.11 Summary 213
PREVIEW
In this chapter, we consider system modeling using time-domain methods. As be-
fore, we will consider physical systems described by an wth-order ordinary differen-
tial equation. Utilizing a (nonunique) set of variables, known as state variables, we
can obtain a set of first-order differential equations. We group these first-order
equations using a compact matrix notation in a model known as the state variable
model. The time-domain state variable model lends itself readily to computer solu-
tion and analysis. The relationship between signal-flow graph models and state vari-
able models will be investigated. Several interesting physical systems, including a
space station and a printer belt drive, are presented and analyzed. The chapter con-
cludes with the development of a state variable model for the Sequential Design
Example: Disk Drive Read System.
DESIRED OUTCOMES
Upon completion of Chapter 3, students should:
• Understand state variables, state differential equations, and output equations.
• Recognize that state variable models can describe the dynamic behavior of physical
systems and can be represented by block diagrams and signal flow graphs.
• Know how to obtain the transfer function model from a state variable model, and vice
versa.
• Be aware of solution methods for state variable models and the role of the state transi-
tion matrix in obtaining the time responses.
• Understand the important role of state variable modeling in control system design.
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