Introducing advanced control methods to undergraduates using a state space model of a synchronous generator

A control systems course at the undergraduate level often focuses on the classical method with only a brief introduction to the state space approach; however, the latter is heavily used in the analysis and design of modern, multivariable control systems. For these students, the state space concept is more difficult to grasp than the classical method due to the computational complexity and lack of graphical representation. This paper provides a basic introduction to state space analysis and design. The principle focus is on a multiple input/multiple output (MIMO) model of a synchronous generator. Using a MIMO system helps students recognize the need for an alternative control system design approach. First, the paper describes and analyzes the physical system and its dynamic behavior using a block diagram. Then, a classical phase lead compensator design, known as a power system stabilizer, along with two optimal controller design approaches, are explained and implemented. The optimal control methods are compared with the classical control approach to show how advanced control design methods yield better transient performance with regards to damping of oscillations and minimization of input energy. A project-based assignment was given to 27 electrical engineering students: construct a state space model of a synchronous generator, implement the various controllers, and compare the results of the optimal control methods to those of a classical control approach based on numerical simulations. Survey results showed that the students agreed with the stated objectives, namely, they understood the importance of using the state space methods and were able to simulate and compare different types of controllers.