Nonlinear Systems
There are different kinds of nonlinearities. For example, on–off control systems are inherently nonlinear. Transport lag, saturation, and transport lag are other kinds of nonlinearities. These kinds of nonlinearities cannot be solved with linear control theory. This is shown in Fig. 1.2. There is complicated theory that covers discontinuous nonlinearities, but they are beyond the scope of this book. Most nonlinearities that exist in servo control systems are shown in Fig. 1.2.
For linearized equation, it is better to use Laplace Transform. In this way, the differential equations become algebraic equation in s. Throughout this book, the lower case s represents Laplace Transform.
Some nonlinearity is continuous, and they can be solved by the linearization technique. One example of this kind of nonlinearity is
