Synthesis of Robust Controller based on Stability Criterion of Forced Oscillations

Abstract

The article is devoted to the development of a classical -synthesis method for a class of nonlinear dynamic systems where nonlinearity is described by harmonic linearization, and the parameters of the harmonic input signal – amplitude and frequency – are specified within certain ranges. The key distinction of the proposed approach from the classical one lies in explicitly accounting for the range of amplitudes and frequencies of the input signal as a synthesis parameter set by an engineer based on operational requirements, rather than implicitly estimating it according to the worst-case scenario. The method relies on the stability criterion of forced oscillations in the first harmonic approximation and transforms the synthesis problem into an amplitude-frequency-explicit design scheme with guaranteed stability bounds. The results are illustrated using an example of servo drive control with saturation nonlinearity and combined dynamic nonlinearity. It is shown that for static nonlinearities, the method provides explicit stability boundaries. For nonlinearities with growing uncertainty, the proposed approach reduces conservatism in estimation: the synthesized controller ensures formal stability guarantees within the operating range of amplitudes, whereas the classical H∞ synthesis with conservative weighting produces values exceeding the stability threshold, indicating inability to certify stability under the same uncertainty description. Thus, the method enables formal stability guarantees within engineer-specified operational ranges by explicitly incorporating amplitude and frequency constraints, thereby reducing conservatism compared to classical worst-case approaches while maintaining compatibility with standard robust control frameworks.