A Nonlinear PID Autotuning Algorithm

A nonlinear autotuning regulator algorithm is obtained via a direct combination of the Åström-Hÿgglund algorithm for the linear case [1] with the sinusoidal-input describing function (SIDEF) approach to nonlinear compensator synthesis of Taylor and Strobel [2]. The basic approach for linear autotuning proceeds as follows: a. install a relay with hysteresis in series with the unknown plant to be controlled; close a unitygain feedback loop around this combination; b. choose several values of hysteresis so that this system exhibits limit cycles; the frequencies and amplitudes of the oscillation at the output of the plant determine points on the plant Nyquist plot; and c. given points on the plant Nyquist plot, set the PID controller gains using an appropriate tuning algorithm (e.g., Ziegler-Nichols). This approach produces good results if the plant is liner or nearly so; however, if the plant behavior is strongly amplitude-dependent, there are likely to be problems with implementing this algorithm. The nonlinear autotuning regulator algorithm which extends the above approach to handle situations where the plant behavior is strongly amplitude-dependent is based on the SIDF approach. In essence, SIDF input/output (I/O) models of the compensated nonlinear system are exploited to directly synthesize a compensator nonlinearity that eliminates or reduces the amplitude dependence of the open-loop I/O relation. The nonlinear synthesis portion of this algorithm is reasonably simple to implement, has been shown to be effective [2], and should be of practical utility. An example application to a precision position control system is provided as an illustration.