Input-output Linearization Problem Research Articles

Input-state feedback linearization for a class of single-input non-linear time-delay systems

In the last decade, a great deal of research has been addressed to the input–output linearization problem for non-linear time-delay systems. However, the input-state linearization problem got much less contributions. In this paper, the input-state linearization problem for a class of single-input non-linear time-delay systems is studied. The problem is solved locally by searching a linearizing output with a full relative degree. Necessary and sufficient conditions are given for the existence of such an output which yields a solution to the full linearization problem.

Input–output linearization of discrete-time systems by dynamic output feedback

The paper addresses the input–output linearization problem by dynamic output feedback for multi-input multi-output nonlinear systems, described by a set of higher order difference equations. Necessary and sufficient solvability conditions are given together with the constructive procedure to check the conditions and compute the feedback.

Modeling and Simulation on Temperature Control System for Hot Pressure Welding

Hot pressure welding (HPW) is one of the inner lead bonding process which is widely used in microelectronics manufacturing. This paper presents a practical digital temperature controller for HPW. Based on the step response, an identification method is developed to obtain a nonlinear time-delay model for heating-up control design. The input-output linearization problem is solved by means of second-order Pade approximation and static inverse transform, and an optimal controller is obtained for the welding machine. The experimental equipment on the temperature control is designed based on LabVIEW and data acquisition card. Simulation and experimental results show that the dynamic performance, steady stage error and overshoot satisfy the designed requirements.

Input–Output Feedback Linearization of Time-Delay Systems

In this note, the input-output linearization problem (IOLP) for a class of single-input-single-output nonlinear systems with multiple delays in the input, the output, and the state is studied. The problem is solved by means of various static or dynamic compensators, including state and output feedback. The mathematical setting is based on some noncommutative algebraic tools and the introduction of a nonlinear version of the so-called Roesser models for this class of systems. These are claimed to be the cornerstones for studying nonlinear time-delay systems. Necessary and sufficient conditions are given for the existence of a static or pure shift output feedback which solves the IOLP. Sufficient conditions for the existence of a dynamic state feedback solution are included as well.

Input-output linearization of retarded non-linear systems by using an extension of Lie derivative

This paper considers the input-output linearization problem for retarded non-linear systems, which have time-delays in the state. By using an extension of the Lie derivative for functional differential equations, we derive a coordinates transformation and a static state feedback to obtain linear input-output behaviour for a class of retarded non-linear systems. The obtained coordinates transformation is allowed to contain not only the current value of the state variables but also the past values of ones. In addition, we show that the coordinates transformation is invertible in a neighbourhood of the origin and examine the stability condition of the closed loop system with the static state feedback. The effectiveness of the proposed technique is demonstrated through numerical simulations.

A Nonlinear Restricted State Feedback Control Strategy for Over-Actuated Robot Manipulators

In the present paper, some recent theoretical results obtained from the analysis of the non-interacting control with simultaneous input-output linearization problem of nonsquare nonlinear systems, using restricted state feedback, are applied to the inverse dynamic control of an over-actuated three-link robot manipulator. The control purpose, in this paper, is to design a nonlinear restricted state feedback control law, such that the generalized coordinates related to links 2 and 3, to be independent of viscous and coulomb friction, and the input-output behavior of the closed-loop system to be I/O linearized and decoupled. The results of the paper offer a new perspective and some new insights to the inverse dynamic control problem of robot manipulators.

On the Input-Output Linearization for Nonlinear Time-Delay Systems

This paper deeds with the input-output linearization problem tor time-delay systems. A new suitable definition for this problem is stated. This work features a sufficient condition for the existence of a static solution, weaker than the conditions found in the literature. The existence of dynamic solutions is investigated as well.

Shortest-prediction-horizon non-linear model-predictive control

This article concerns non-linear control of single-input-single-output processes with input constraints and deadtimes. The problem of input-output linearization in continuous time is formulated as a model-predictive control problem, for processes with full-state measurements and for processes with incomplete state measurements and deadtimes. This model-predictive control formulation allows one (i) to establish the connections between model-predictive and input-output linearizing control methods; and (ii) to solve directly the problems of constraint handling and windup in input-output linearizing control. The derived model-predictive control laws have the shortest possible prediction horizon and explicit analytical form, and thus their implementation does not require on-line optimization. Necessary conditions for stability of the closed-loop system under the constrained dynamic control laws are given. The connections between (a) the developed control laws and (b) the model state feedback control and the modified internal model control are established. The application and performance of the derived controllers are demonstrated by numerical simulations of chemical and biochemical reactor examples.

非線形システムの近似入出力線形化

We will define an approximate input-output linearization problem -- an order ? input-output linearization problem. To solve this, we must find a feedback u=?(x)+s(x)v for the system x=f(x)+g(x)u, y =h(x) such that the input-output response will be order ? input-output linear, i.e. its Volterra series expansion (V.S.E.) will be y(t) = W0(t) + ?i=1 m ?0 t{?p=0 ?K(i,p)(t-?)p/p!}vi(?)d? +?j=1 ?W(?+j) where W(k) is k-th order term of V.S.E. This system will be approximately linear if the kernels of order larger than ? are negligible. We will identify, using a modified structure algorithm, the class of nonlinear systems which can be transformed into order ? input-output linear systems. We will also show that, under suitable conditions, an order ? input-output linear system can be expressed in an appropriate state as ? = F? + Gv +od(?, ?, v)?+1 ? = f?(?, ?) + ?(?, ?)v y = H? where F, G and H are matrices of real numbers.

On input-output linearization of discrete-time nonlinear systems

We consider a nonlinear discrete-time system of the form Σ: x( t+1)= f( x( t), u( t)), y( t) = h( x( t)), where x ϵ R N , u ϵ R m , y ϵ R q and f and h are analytic. Necessary and sufficient conditions for local input-output linearizability are given. We show that these conditions are also sufficient for a formal solution to the global input-output linearization problem. Finally, we show that zeros at infinity of ϵ can be obtained by the structure algorithm for locally input-output linearizable systems.