Probabilistic evaluation of control system robustness†

Practical control systems must operate satisfactorily with uncertain variations in plant parameters (i.e., control systems must be robust), but there are limits to the degree of robustness that may be considered desirable. Tolerance to parameter variations that never occur is not useful, and it could lead to closed-loop systems whose normal performance has been compromised unnecessarily. A probabilistic definition of robustness based on expected parameter variations is consistent with accepted design principles, and it is readily evaluated by simulation. Stochastic Robustness Analysis predicts the effects of likely parameter variations on closed-loop stability and performance through evaluation of commonly accepted criteria. Competing control designs are judged by the likelihood that system response and design metrics will fall within desired bounds. Together with numerical search, probabilistic evaluation is a powerful approach not only for comparing alternative controllers but for designing control systems that satisfy robustness and performance requirements.