Quasilinear Control Theory for Systems with Asymmetric Actuators and Sensors

The theory of Quasilinear Control (QLC) is a set of methods for analytical design of controllers for Linear Plant Nonlinear Instrumentations (LPNI) systems, where the term “instrumentation” is used to denote actuators and sensors. In practice, controllers for LPNI systems are often designed ignoring instrumentation nonlinearities (e.g., saturation, quantization, dead zones, etc.) and then calibrated using hardware-in-the-loop. QLC provides analytical tools to accomplish this. The approach is based on the method of Stochastic Linearization, which reduces static nonlinearities to a quasilinear gain. Unlike the usual (Jacobian) linearization, Stochastic Linearization is global. The price to pay is that the quasilinear gain depends not only on the operating point, but also on the exogenous signals and functional blocks of the closed-loop system. Using this approach, QLC theory has extended practically all methods of Linear Control theory to LPNI systems. This includes the notions of system types, error coefficients, root-locus, LQR/LQG, H∞, etc. In addition, LPNI-specific problems have been addresses (e.g., partial and complete performance recovery). The main results of QLC have been summarized in a textbook (Cambridge University Press, 2011) and presented at the Technion in 2011. In the current talk, after a brief overview of the previous results, we center on new ones, specifically on the phenomena, arising in systems with asymmetric nonlinearities (i.e., a generic case of tracking problems with saturating actuators).