Design of Feedback Control Systems

While being highly successful, the classical control theory is limited in its applications to primarily single-input/single-output (SISO) systems due to the graphical nature of its design tools such as methods of Bode and root locus. For multi-input/multioutput (MIMO) systems it is the modern control theory that grows into a mature design methodology, termed as linear quadratic Gaussian (LQG) optimal control. It assumes a linear state-space model for the underlying multivariable system with stochastic descriptions for exogenous noises and disturbances impinged on the feedback system. The performance index is a combination of the mean powers of the control input and error signal. Minimization of the performance index is the design objective that admits a closed-form solution for the optimal feedback controller.LQG control was motivated largely by the space program massively funded in the 1950s. It had a huge success in space applications because accurate models can be developed for space vehicles, white noise descriptions are appropriate for external disturbances, and the fuel consumption is crucial in space missions. Owing to the work of Kalman and other scientists, LQG control has since become an effective design methodology for multivariable feedback control systems. This chapter considers H2 optimal control that is modified from the LQG control focusing on linear time-invariant systems. The optimal solution to linear quadratic control will be derived for the case of output feedback rather than state feedback. Design of multivariable feedback control systems will then be studied with the objective to satisfying performance specifications in frequency and time domains. Design tools such as frequency loop shaping and eigenvalue assignment will be developed which can be regarded as extension of Bode and root locus in classic control, respectively. Various other design issues such as controller reduction and stability margins will be investigated as well.