Dynamic Systems and Control Engineering

Recall from our discussions in Part II that dynamic systems can be represented through various mathematical modeling strategies, including systems of ordinary differential equations, systems of Laplace-domain equations, transfer functions, functional block diagrams, and physical models. Through our review of the Laplace domain, we found that the zero-state input–output behavior of dynamic systems could be represented, conveniently, as the ratio of the system’s Laplace-domain output and its Laplace-domain input. These ratios, or transfer functions, simplified our analysis of interconnected systems and enabled the design of feedback control systems in Part III. However, while the Laplace-domain and transfer functions are undoubtedly powerful and useful tools for systems with a single input and a single output, known as(SISO) systems, the implementation of transfer functions can become cumbersome and complex for systems with multiple inputs and multiple outputs, known as(MIMO) systems.