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

We investigate Quasilinear Control (QLC) of time-delay systems with nonlinear actuators and sensors. QLC leverages the method of stochastic linearization to replace each nonlinearity with an equivalent gain. The existence of the equivalent gain for a closed loop time-delay system is discussed. To compute the equivalent gain, both the delay Lyapunov method and the Padé approximant are explored. The method of saturated-root locus (S-RL) is extended to nonlinear time-delay systems, and a QLC-based optimal controller design is presented. Statistical experiments are performed to investigate the accuracy of stochastic linearization compared to a system without time-delay. Results show that stochastic linearization effectively linearizes a nonlinear time-delay system, even though delays generally degrade accuracy. Finally, pitch control in a wind turbine system is introduced as a practical example of a nonlinear time-delay system, and its performance is analyzed to demonstrate the applicability and efficacy of the approach.