Identifying limits of linear control design validity in nonlinear systems: a continuation-based approach

Abstract It is well known that a linear-based controller only valid near the point from which linearised system obtained. The question remains as to how far one can move away before linear and nonlinear responses differ significantly, resulting in failing achieve desired performance. In this paper, we propose method quantify these differences. By appending harmonic oscillator equations of motion, frequency at different operating points be generated using numerical continuation. presence strong nonlinearities, subtle differences exist between responses, variations are also reflected step responses. A systematic way comparing discrepancies presented, determine whether performs predicted by design. We demonstrate on simple fixed-gain Duffing gain-scheduled reduced-order aircraft model with manoeuvre-demand controller; latter presents case where nonlinearities form multiple attractors. analysis then expanded include actuator rate saturation, creates limit-cycle isola, coexisting solutions (corresponding so-called flying qualities cliff), chaotic motions. proposed infer influence additional attractors even when there no detect them. Finally, severe saturation present, reducing gains mitigate—but not eliminate—the risk oscillation.