Anderson B., Moore J. Optimal Control: Linear Quadratic Methods

Prentice-Hall International, 2007. — 405 p.The methods and techniques of what is now known as "classical control" will be familiar to most readers. In the main, the systems or plants that can be considered by using classical control ideas are linear and time invariant, and have a single input and a single output. The primary aim of the designer using classical control design methods is to stabilize a plant, whereas secondary aims may involve obtaining a certain transient response, bandwidth, disturbance rejection, steady state error, and robustness to plant variations or uncertainties. The designer's methods are a combination of analytical ones (e.g. , Laplace transform, Routh test), graphical ones (e.g. , Nyquist plots, Nichols charts), and a good deal of empirically based knowledge (e.g. , a certain class of compensator works satisfactorily for a certain class of plant). For higher-order systems, multiple-input systems, or systems that do not possess the properties usually assumed in the classical control approach, the designer's ingenuity is generally the limiting factor in achieving a satisfactory design. Two of the main aims of modern, as opposed to classical, control are to de-empiricize control system design and to present solutions to a much wider class of control problems than classical control can tackle. One of the major ways modern control sets out to achieve these aims is by providing an array of analytical design procedures that facilitate the design task.