Quasilinear Control

Abstract

This is a textbook and reference for readers interested in quasilinear control (QLC). QLC is a set of methods for performance analysis and design of linear plant or nonlinear instrumentation (LPNI) systems. The approach of QLC is based on the method of stochastic linearization, which reduces the nonlinearities of actuators and sensors to quasilinear gains. Unlike the usual - Jacobian linearization - stochastic linearization is global. Using this approximation, QLC extends most of the linear control theory techniques to LPNI systems. A bisection algorithm for solving these equations is provided. In addition, QLC includes new problems, specific for the LPNI scenario. Examples include Instrumented LQR/LQG, in which the controller is designed simultaneously with the actuator and sensor, and partial and complete performance recovery, in which the degradation of linear performance is either contained by selecting the right instrumentation or completely eliminated by the controller boosting.

Quasilinear control approach to wind farm power control

“…The QLC theory utilizes stochastic linearization [15] to replace each nonlinearity in the system with an equivalent gain and an equivalent bias. As it is shown in [13], [14], the resulting quasilinear system is capable of closely approximating signals in the original nonlinear system if the plant has sufficient low-pass filtering characteristics, which, as we show, is the case with the WTCS model considered in this paper. Since QLC takes into account the actuator nonlinearity in the design and analysis stage, it is expected to yield a better performance compared to the existing, linear method in [12].…”

“…Hence, by applying an optimization algorithm to (12) and (13), the K i 's that minimize J may be determined, completing the final step of the WFC design.…”

“…In [13], [14], it is shown that if the plant has sufficiently slow dynamics as compared with the bandwidth of the exogenous signals, then the quasilinear system provides a faithful estimate of the mean and variance of the output of the original LPNI system. QLC Theory takes advantage of this fact and provides methods for designing controllers for LPNI systems.…”

“…To alleviate this drawback, in this paper we leverage the recently-developed theory of Quasilinear Control (QLC) [13], [14], which provides methods for performance analysis and controller design of systems with static nonlinearities in actuators and sensors. The QLC theory utilizes stochastic linearization [15] to replace each nonlinearity in the system with an equivalent gain and an equivalent bias.…”

Quasilinear Control of Systems with Time-Delays and Nonlinear Actuators and Sensors

“…Unlike nonlinear plants, which can often be linearized to operate at a desired operating point in a well-designed control system, the actuators and sensors cannot, especially when required to operate far from their initial conditions due to large inputs to the system. We refer to this class of systems as Linear Plant/Nonlinear Instrumentation Recently, [3] developed the Quasilinear Control theory (QLC), which extended the classical linear control theory to LPNI systems. The analysis and synthesis equations in QLC remain essentially the same as in the linear control except for additional transcendental equations, which are used for computing an equivalent gain in place of the nonlinear instrumentation.…”