Quasilinear Control of Systems with Asymmetric Actuators and Sensors

Abstract: Quasilinear Control (QLC) theory provides a set of methods for analysis and design of systems with nonlinear actuators and sensors. Two ubiquitous nonlinearities are actuator saturation and sensor deadzone. One limitation of the current QLC theory is that it is applicable only to systems with symmetric nonlinearities. In many situations, however, nonlinearities are asymmetric. Examples of such systems abound: heating systems, automotive torque control, wind turbine control, etc. In this work, we provide an extension of the QLC theory to the asymmetric case. The approach is based on the method of stochastic linearization, which replaces each nonlinear element by an equivalent gain and an equivalent bias. The latter leads to steady state errors incompatible with the usual error coefficients, which makes the asymmetric case a non-trivial extension of the symmetric one. Specific problems addressed in this dissertation with regards to asymmetric systems are: (i) Introduction of the notion of asymmetry. (ii) Development of a formalism of stochastic linearization for asymmetric systems.(iii) Analysis of tracking and disturbance rejection performance. (iv) Time domain design of tracking controllers. (vi) Recovery of linear performance in nonlinear systems. (vii) Disturbance rejection controller design using an LQR-type approach. (viii) Application of the developed methods to a wind farm controller design.