ABSTRACT
This chapter considers the problem of designing an optimal control system. The optimal control strategy will thus be a trade-off between excessive deviations of the system and excessive control efforts. The minimization of the performance index must be compatible with the constraints imposed by the dynamics of the plant to be controlled. The chapter aims to develop the control strategy that minimizes an objective function which is quadratic in the system state variables and the control efforts. This control strategy was one that constructed the control efforts as a linear combination of the state variables. The eigenvalues of the adjoint system and plant are shown to occur in reciprocal pairs, and the reciprocal root locus is given as a tool to guide the selection of performance indices for single-input/single-output systems in terms of desired control system pole locations. In a large number of applications it is desirable to control deviations of the system output about some fixed value.
