TABLE OF CONTENTS In this chapter, I introduce techniques for developing linear time-invariant plant models. This type of model provides a simplified representation of the dynamic behavior of a real-world system. The control system design methods covered in subsequent chapters require plant models of this type. Linear time-invariant models possess a number of desirable mathematical properties that the upcoming design methods will utilize.
The standard approach for developing linear time-invariant models taught in engineering courses is to apply the laws of physics to a given system and develop a set of differential equations describing its behavior. The resulting equations are often nonlinear, so an additional step must be performed to linearize them. Linearization is the development of a set of linear equations that approximate the nonlinear equations in the vicinity of an equilibrium point. An equilibrium point is an operating point where the system is in a steady state and all the derivatives in the equations are zero. In many systems of interest, the response of the plant to small perturbations about an equilibrium point is approximately linear.
An example of an equilibrium point is an automobile operating under cruise control that is traveling at a steady speed on a level road. Because the vehicle speed is constant, the acceleration (the derivative of the speed) is zero.
The physics-based approach works well when the designer possesses the mathematical and engineering background to perform the analysis and linearization procedures. However, it is often the case that insufficient information exists...
