State space control

Classical design of digital controllers involves the use of frequency domain methods and the root locus. Control is restricted to single-input, single-output systems. The aim of this chapter is to introduce the state space or modern approach to design. Although single-input, single-output systems will mainly be considered, modern control design can readily be extended to cover systems with several inputs and outputs. The design of state feedback controllers is presented after a brief introduction to state space models including the key ideas of controllability and observability. The selection of feedback gains in order to achieve a desired set of closed-loop poles will be familiar to engineers versed with classical design methods. The implementation of state feedback control laws assumes that all the state variables are known. In practice, the state vector is estimated from the measurements or plant outputs using an observer. Observer design is therefore treated next prior to an analysis of the complete control-estimator system.