A new systematic and algebraic linear control system design procedure for use with highly nonlinear plants is developed. This procedure is based on simultaneous stabilization theory and sinusoidal-input describing function models of the nonlinear plant, and is presently applicable to single-input single-output, time-invariant, deterministic, stable, and continuous-time systems which are representable in standard state-variable differential equation form. Three software utilities to implement the controller design procedure are also outlined. This method and the associated software is applied to a position control problem of the sort encountered in robotics, and the results are compared with those previously obtained using both linear and nonlinear PID control.
Controller Design For Nonlinear Systems Based on Simultaneous Stabilization Theory and Describing Function Models
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Nassirharand, A., Taylor, J. H., and Reid, K. N. (June 1, 1988). "Controller Design For Nonlinear Systems Based on Simultaneous Stabilization Theory and Describing Function Models." ASME. J. Dyn. Sys., Meas., Control. June 1988; 110(2): 134–142. https://doi.org/10.1115/1.3152663
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