Frequency-domain stability conditions for split-path nonlinear systems

This paper considers the class of control systems containing so-called split-path nonlinear (SPAN) filters, which are designed to overcome some of the well-known fundamental limitations in linear time-invariant (LTI) control. In this work, we are interested in developing tools for the stability analysis of such systems using frequency-domain techniques. Hereto, we explicitly show the equivalence between a set of linear matrix inequalities (LMIs) with S-procedure terms, guaranteeing stability of the closed-loop (SPAN) system, and a frequency-domain condition. We also provide a systematic procedure for verifying the frequency-domain condition in a graphical manner. The results are illustrated through a nummerical case study.</p

Filtered Split-Path Nonlinear Integrator (F-SPANI) for improved transient performance

\u3cp\u3eThe recently introduced Split-Path Nonlinear Integrator (SPANI) is designed to improve the transient performance of linear (motion) systems in terms of overshoot. The SPANI was shown to be an effective nonlinear controller to improve transient performance by enforcing the same sign in the integrator action and the error. However, to avoid (fast) switching in the control input in steady-state, conservatism had to be introduced in the SPANI design, thereby limiting the performance. In this paper, this conservatism is removed by introducing a new design, called the Filtered Split-Path Nonlinear Integrator (F-SPANI). This design is based on the inclusion of an additional filter in the phase path, which enables the full potential behind the main idea of the SPANI. The ease of the design and implementation and the potential of the proposed controller are illustrated both in simulation and in experiments on a motion system.\u3c/p\u3

Filtered Split-Path Nonlinear Integrator (F-SPANI) for improved transient performance

The recently introduced Split-Path Nonlinear Integrator (SPANI) is designed to improve the transient performance of linear (motion) systems in terms of overshoot. The SPANI was shown to be an effective nonlinear controller to improve transient performance by enforcing the same sign in the integrator action and the error. However, to avoid (fast) switching in the control input in steady-state, conservatism had to be introduced in the SPANI design, thereby limiting the performance. In this paper, this conservatism is removed by introducing a new design, called the Filtered Split-Path Nonlinear Integrator (F-SPANI). This design is based on the inclusion of an additional filter in the phase path, which enables the full potential behind the main idea of the SPANI. The ease of the design and implementation and the potential of the proposed controller are illustrated both in simulation and in experiments on a motion system