Control of nonlinear non-minimum phase systems with input-output linearization

Abstract

In this paper we present a new approach of using input-output linearization to control a single input, single output, input-affine nonlinear non-minimum phase system. We will show that, if the linearized system is stabilizable, we can redefine the output of the system such that the input-output linearized system is locally asymptotically stable. Furthermore we develop an LQR technique for designing the redefined output, which assures stabilization of the zerodynamics. Simulations of a physical system show that the resulting controller, which in a way fuses LQR techniques with input-output linearization, outperforms a regular LQR feedback controller and demonstrates a big region of attraction. The presented technique can be used to regulate the system around an equilibrium and to achieve tracking for certain trajectories. Conditions are established that allow the asymptotic regulation and tracking of desired trajectories for the original output. We will demonstrate the control design on a two-dimensional Segway model.

Discrete sliding mode control with optimal generalized sliding function for non-minimum phase system

“…NMPS admits one of the zeros of its transfer function unstable. This property restricts the direct application of many powerful nonlinear control techniques, such as backstepping control, 6,7 feedback linearization 8,9 and sliding mode control (SMC). 10–12…”

“…NMPS admits one of the zeros of its transfer function unstable. This property restricts the direct application of many powerful nonlinear control techniques, such as backstepping control, 6,7 feedback linearization 8,9 and sliding mode control (SMC). [10][11][12] Therefore, the presence of the unstable zero risks to deteriorate or saturate the control law 13 as it is an important source of poor performance and instability.…”

Tracking control for planar nonminimum-phase bilinear control system with disturbance using backstepping

“…Even though the system contains uncertainty, the absence of internal dynamics makes it possible to design controls directly on the system. We applies backstepping to the normal form obtained through the input-output linearisation transformation using the procedure in [38], [39]. Since there are internal dynamics, they will be stabilised first using virtual controls.…”

Adaptive approximate input–output linearizing control with applications to ball and beam mechanism

“…An approximate input–output linearizing control method, presented by Hauser et al (1992), suggested a control strategy relying on an input–output linearizable approximation for the system. The method has attracted the attention of researchers and led to several other designs and applications (Deutscher, 2005; Ho and Hedrick, 2015; Kim and Oh, 1999; Leith and Leithead, 2001; Xiang and Wikander, 2004). Some of these applications include an adaptive approach to the method (Ghanadan and Blankenship, 1996; Kanellakopoulos et al, 1991; Ko et al, 1999; Kwon and Choi, 2014; Marino, 1997; Mohammed et al, 2012; Raimundez et al, 2014; Sahnehsaraei et al, 2014).…”