Linear Control

Abstract

In this chapter, the concept of linear negative feedback is introduced, and the topic of stability is revisited. The primary focus is on assessing the effect of time delay in applying the control force on the stability. Subsequently, the choice of the optimal magnitudes of the feedback parameters is considered. Optimality is related to the magnitude of a quadratic performance index, which is taken as a time integral involving weighted response and control force terms. This approach is referred to as the linear quadratic regulator (LQR) problem and leads to a time-invariant linear relationship between the control forces and state variables. Finally, we discuss optimal feedback based on the LQR performance index generalized for multi-degree-of-freedoms systems. Examples that illustrate the sensitivity of the response and cost parameters to variations in the location and nature of the control forces and weighting coefficients are presented. We end the chapter with a brief discussion of advanced topics for time-invariant control.