Improved Statistical Linearization for Analysis and Control of Nonlinear Stochastic Systems: Part II: Application to Control System Design

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Using the techniques of Gaussian statistical linearization and the extension given in Part I, this paper describes the synthesis of linear feedback controllers for nonlinear stochastic systems. The method used is that of pole placement of the statistically linearized “eigenvalues”. The technique is described in terms of a design example, a position servomechanism with backlash, it is shown that for this type of system the standard Gaussian method works well for large input noise levels but can lead to an unstable design for low input levels. The extended fourth cumulant method is satisfactory for both cases studied. The results of the analysis are compared to Monte Carlo digital simulations to test their accuracy.