Process Control: A First Course with MATLAB
Written from the perspective of a student, this text emphasizes the importance of computers in the modern age of teaching and practicing process control.
TABLE OF CONTENTS Process Control: A First Course with MATLAB
Chapter 9: Design of State-Space Systems
We now return to the use of state-space representation that was introduced in Chap. 4. As you may have guessed, we want to design control systems based on state-space analysis. A state feedback controller is very different from the classical PID controller. Our treatment remains introductory, and we will stay with linear or linearized SISO systems. Nevertheless, the topics here should enlighten (!) us as to what modern control is all about.
What Are We Up to?
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Evaluating the controllability and observability of a system.
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Designing pole placement of state feedback systems. Applying Ackermann's formula.
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Designing with full-state and reduced-order observers (estimators).
9.1. Controllability and Observability
Before we formulate a state-space system, we need to raise two important questions. One is whether the choice of inputs (the manipulated variables) may lead to changes in the states, and the second is whether we can evaluate all the states based on the observed output. These are what we call the controllability and the observability problems.
9.1.1. Controllability
A system is said to be completely state controllable if there exists an input u( t) that can drive the system from any given initial state x 0( t 0 = 0) to any other desired state x( t). To derive the controllability criterion, let us restate the linear system and its solution from Eqs. (4.1), (4.2), and (4.10):
| (9.1) |  |
| (9.2) |  |
| (9.3) |  |
With our definition of controllability, there is no loss of generality if we choose to have x( t
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