Funnel Control With Saturation: Nonlinear SISO Systems $ $

Abstract

Tracking-by the system output-of a reference signal (assumed bounded with essentially bounded derivative) is considered in the context of a class of nonlinear, single-input, single-output systems modelled by functional differential equations and subject to input saturation. Prespecified is a parameterized performance funnel within which the tracking error is required to evolve; transient and asymptotic behaviour of the tracking error is influenced through choice of parameter values which define the funnel. The control structure is a saturating error feedback with time-varying non-monotone gain designed to evolve in such a way as to preclude contact with the funnel boundary. A feasibility condition-formulated in bounds of the plant data, the saturation bound, the funnel data, the reference signal and the initial data-is presented under which the tracking objective is achieved, whilst maintaining boundedness of the state and gain function.

Funnel control for speed & position control of electrical drives: A survey

“…Funnel control with saturation is possible, see the theoretical results in e.g. [26], [27], [11], [21] for relative degree one and two: a (possibly very) conservative feasibility condition gives a sufficient lower bound on the required control input, however this bound is often not reasonable for application. More realistic and intuitive results for the relative-degreeone case -but only empirically examined -are proposed in [7], [5].…”

Three-dimensional sliding mode guidance law for maneuvering target with prescribed performance and input saturation

“…This is a continuation of the adaptive high-gain control methodology that replaces the monotonically increasing control gain with a time-varying function. When the output error of the system is close to the funnel boundary, the funnel control admits high values, resulting in a simple nonlinear and time-varying proportional control scheme for classes of nonlinear systems with a known relative degree of one (Hopfe et al, 2010; Ilchmann and Ryan, 2009; Ilchmann et al, 2005, 2010) and, more recently, two (Hackl et al, 2010; Reis and Berger, 2017). In Bu (2018), a funnel non-affine controller for AHVs with prescribed performance was proposed applying neural approximation.…”

Robust output tracking of nonlinear systems with transient improvement via funnel-based sliding mode control

“…Moreover, the proposed controller can obviate the chattering phenomenon and also remove the steady-state tracking error. On the other hand, funnel-based control is usually implemented as a coefficient of tracking error (Berger, 2016; Hopfe et al, 2010). However, in this paper, the funnel-based control has designed as a time-varying coefficient of the sliding surface.…”