State Feedback

Feedback is a fundamental principle in automatic control of dynamic processes and systems in many application areas. A properly designed feedback can achieve that the closed-loop system is stable and meets performance and robustness requirements. This chapter discusses state feedback. The presentation starts with the design of a static feedback gain matrix for fully state controllable SISO systems in controller canonical form on the basis of assigned closed-loop poles obtained from behaviour requirements. To ensure reference tracking, state feedback is extended by means of a PI controller. For MIMO systems, various feedback gain matrices may ensure that the closed-loop system has prescribed eigenvalues. One approach to systematically find a state-feedback matrix for MIMO systems with more than one input is the cyclic design procedure. If a MIMO system is not completely state controllable, it can be transformed into controllable form which also indicates whether the uncontrollable can be stabilised. In general, it is impractical or even impossible to measure all states so that missing components of the state vector must be reconstructed. The chapter presents the design of a full-order observer and the separation principle import for an observer-based state feedback. To avoid a high-order controller with an embedded observer, the construction of a reduced observer is outlined. Finally, the behaviour of an observer in the presence of disturbances and unknown input observers is discussed. Noisy measurements are addressed in Sect. 10.3 on Kalman filters.