Input-output Linearization Of Nonlinear Systems Research Articles

A Further Result on Semi-global Stabilization of Minimum-Phase Input–Output Linearizable Nonlinear Systems by Linear Partial State Feedback

It has been established that a globally asymptotically stable nonlinear system cascaded by a controllable linear system through its output can be semi-globally asymptotically stabilized by linear feedback of the state of the linear subsystem as long as the linear system is right invertible and has all its invariant zeros located on the closed left-half plane. In particular, a globally asymptotically stable nonlinear system cascaded by a chain of integrator through the state of any one integrator or the control input is semi-globally asymptotically stabilizable by linear feedback of the states of the integrators. In this note, we show that the restriction on the interconnection between the linear and nonlinear subsystems can be further relaxed. For example, a globally asymptotically stable nonlinear system cascaded by a chain of integrator can still be semi-globally stabilized even when the cascade is through the states of two consecutive integrators, with the input regarded as an additional state following the last integrator.

Multi‐parametric extremum seeking‐based iterative feedback gains tuning for nonlinear control

SummaryWe study in this paper the problem of iterative feedback gains auto‐tuning for a class of nonlinear systems. For the class of input–output linearizable nonlinear systems with bounded additive uncertainties, we first design a nominal input–output linearization‐based robust controller that ensures global uniform boundedness of the output tracking error dynamics. Then, we complement the robust controller with a model‐free multi‐parametric extremum seeking control to iteratively auto‐tune the feedback gains. We analyze the stability of the whole controller, that is, the robust nonlinear controller combined with the multi‐parametric extremum seeking model‐free learning algorithm. We use numerical tests to demonstrate the performance of this method on a mechatronics example. Copyright © 2016 John Wiley & Sons, Ltd.

Robust control approach for input–output linearizable nonlinear systems using high‐gain disturbance observer

SUMMARYThis paper addresses a robust control approach for a class of input–output linearizable nonlinear systems with uncertainties and modeling errors considered as unknown inputs. As known, the exact feedback linearization method can be applied to control input–output linearizable nonlinear systems, if all the states are available and modeling errors are negligible. The mentioned two prerequisites denote important problems in the field of classical nonlinear control. The solution approach developed in this contribution is using disturbance rejection by applying feedback of the uncertainties and modeling errors estimated by a specific high‐gain disturbance observer as unknown inputs. At the same time, the nonmeasured states can be calculated from the estimation of the transformed system states. The feasibility and conditions for the application of the approach on mechanical systems are discussed. A nonlinear multi‐input multi‐output mechanical system is taken as a simulation example to illustrate the application. The results show the robustness of the control design and plausible estimations of full‐rank disturbances.Copyright © 2012 John Wiley & Sons, Ltd.

Adaptive internal model control of nonlinear processes

Model-based controllers are often essential for effective control of nonlinear processes. Performance and robustness of these controllers are affected by the inevitable modeling errors, and parameter adaptation is a technique to robustify the model-based controllers. In this paper, an adaptive internal model control (AdIMC) for a class of minimum-phase input–output linearizable nonlinear systems with parameter uncertainty is presented. Internal model control (IMC) for nonlinear systems is developed directly from input–output linearization. The parameter adaptation for the IMC is based on process and model outputs, and the state variables predicted by the model only. Asymptotic tracking and convergence of unknown parameters by the proposed adaptation, is first shown theoretically. Then, AdIMC is applied to two nonlinear processes (a fermentor and a neutralization process), and its performance for a variety of disturbances and modeling errors is studied. The theoretical and simulation results show that the proposed AdIMC improves the performance and robustness of the IMC controller for nonlinear processes. Also, the proposed adaptation can easily be implemented in the IMC structure.

Robust adaptive control of nonlinear systems subjected to system uncertainties

In this work, the adaptive control scheme for a class of input-output linearizable nonlinear systems subjected to system uncertainties is presented. An adaptation law is proposed to estimate unknown system parameters such that the effect of the system parameter uncertainties can be reduced and a switching state feedback gain is set in the adaptive control input to treat with unmodelled dynamical uncertainty problems. Then a robust adaptive control scheme in the presence of the above system uncertainties can be ensured. It is further indicated that the proposed adaptive control scheme will be robust asymptotically stable under some modifications. Some computer simulation results are proposed to show the performance of the proposed adaptive control scheme.

On the input-output linearization of nonlinear systems

This paper exposes two different possible definitions of input-output linearization of nonlinear systems and gives the corresponding necessary and sufficient conditions for their solvability.

Input-output linearization of nonlinear systems with time delays in state variables

The present paper is concerned with nonlinear systems that contain delays inside coupled with a part of state variables, which are often the cases in practical problems, but have not been treated yet. First we introduce an extension of the Lie derivative for a difference-differential equation; then we derive necessary and sufficient conditions for existence of a nonlinear feedback that linearizes the input-output behaviour of a system and decouples it from the delayed variables simultaneously. Discussions are given for two cases: firstly when the linearizing feedback contains only current values of state variables, and secondly when the linearizing feedback has memories to utilize the past values as well as the current values of state variables.

DYNAMICAL ADAPTIVE SLIDING MODE OUTPUT TRACKING CONTROL OF A CLASS OF NONLINEAR SYSTEMS

An alternative adaptive scheme to achieve output tracking for a class of minimum-phase dynamically input–output linearizable nonlinear systems with parametric uncertainties is considered. The proposed approach is based upon a combination of the adaptive backstepping design method and a sliding mode control (SMC) scheme to design dynamical adaptive sliding mode controllers and provide robust output tracking even in the presence of unknown disturbances. The validity of the proposed approach, regarding tracking objectives and robustness with respect to bounded stochastic perturbation inputs, is tested through digital computer simulations. © 1997 by John Wiley & Sons, Ltd.

DYNAMICAL ADAPTIVE SLIDING MODE OUTPUT TRACKING CONTROL OF A CLASS OF NONLINEAR SYSTEMS

An alternative adaptive scheme to achieve output tracking for a class of minimum-phase dynamically input–output linearizable nonlinear systems with parametric uncertainties is considered. The proposed approach is based upon a combination of the adaptive backstepping design method and a sliding mode control (SMC) scheme to design dynamical adaptive sliding mode controllers and provide robust output tracking even in the presence of unknown disturbances. The validity of the proposed approach, regarding tracking objectives and robustness with respect to bounded stochastic perturbation inputs, is tested through digital computer simulations. © 1997 by John Wiley & Sons, Ltd.

Matching conditions for stability analysis of nonlinear feedback control systems

The differential geometry approach for exact input-output linearizable nonlinear systems usually results in a complicated nonlinear controller that is difficult to implement. To overcome this difficulty, we propose to approximate the nonlinear controller by a canonical piecewise linear expression within an allowable error bound. This design procedure can reduce a tremendous amount of computation in the design and the synthesis. The resulting controller turns out to be fairly simple in general and can achieve many performance specifications. Some sufficient conditions for guaranteeing the closed-loop system stability using this controller design method is derived in the present paper. An application to a chemical reactor system is also briefly discussed.

Nonlinear control via approximate input-output linearization: the ball and beam example

Approximate input-output linearization of nonlinear systems which fail to have a well defined relative degree is studied. For such systems, a method for constructing approximate systems that are input-output linearizable is provided. The analysis presented is motivated through its application to a common undergraduate control laboratory experiment-the ball and beam-where it is shown to be more effective for trajectory tracking than the standard Jacobian linearization. >

Indirect techniques for adaptive input-output linearization of non-linear systems

Abstract A technique of indirect adaptive control based on certainty equivalence for input output linearization of non-linear systems is proven convergent. It does not surfer from the overparameterization drawbacks of the direct adaptive control techniques on the same plant. This paper also contains a semi-indirect adaptive controller which has several attractive features of both the direct and indirect schemes