Class Of Reference Signals Research Articles

Asymptotic tracking control for a class of reference signals for linear differential inclusions

Tracking control for linear differential inclusions with disturbances is investigated in this paper. Based on the convex hull Lyapunov function, a feedback control law is designed such that the output of the closed-loop system without disturbances globally asymptotically tracks the desired reference signal. Under the bounded disturbances, the tracking error is bounded. An example is given to illustrate how to make the output of the closed-loop system track a sinusoidal signal, a cosine signal and a circular signal. The simulation shows the effectiveness of the proposed method.

Asymptotic tracking with prescribed transient behaviour for linear systems

The problem of asymptotic tracking of reference signals is considered in the context of m-input, m-output linear systems (A,B,C) with the following structural properties: (i) CB is sign definite (but not necessarily symmetric), (ii) the zero dynamics are exponentially stable. The class of reference signals is the set of all possible solutions of a fixed, stable, linear, homogeneous differential equation (with associated characteristic polynomial α). The first control objective is asymptotic tracking, by the system output y = Cx, of any reference signal . The second objective is guaranteed error e = y − r transient performance: e should evolve within a prescribed performance funnel (determined by a function ϕ). Both objectives are achieved simultaneously by an internal model in series with a proportional time-varying error feedback t↦ u(t)=−ν (k(t)) e(t), where ν is a smooth function with the properties and , and k(t) is generated via a nonlinear function of the product ‖ e(t)‖ ϕ (t) The feedback structure essentially exploits an intrinsic high-gain property of the system by ensuring that, if (t,e(t)) approaches the funnel boundary, then the gain attains values sufficiently large to preclude boundary contact.

Adaptive state feedback control by orthogonal approximation functions

AbstractFor a class of feedback linearizable systems a state feedback adaptive control based on orthogonal approximation functions is designed, under the assumption of matching conditions for the uncertainties and of known bounds on a given compact set for the unknown non‐linear function. By virtue of Bessel inequality, the bound on the unknown non‐linear function gives a bound on the norm of the optimal weight vector for any choice of the number of approximating functions, which allows us to design a robust state feedback adaptive scheme with parameter projections. The resulting control algorithm has several advantages over available schemes: it does not require a priori bounds on the approximation error and on the optimal weight vector; it is repeatable, since the set of initial conditions for the state and the parameter estimates from which a class of reference signals is tracked is explicitly given; it characterizes the L∞ and L2 performance of the tracking error in terms of both the approximation and the parameter estimation error; it gives full flexibility in the choice of the number of approximating orthogonal functions. Copyright © 2002 John Wiley & Sons, Ltd.

Simple robust output-feedback controller for uncertain nonlinear systems

A robust output-feedback controller is designed by using an observer plus backstepping procedure to solve the tracking problems of a class of uncertain nonlinear systems. In the design procedure, three techniques are applied: a) a single filter whose dynamic order is the same as the system order is constructed; b) a normalization signal is introduced; c) positive nonlinear functions that are used to generate the normalization signal and to construct nonlinear damping terms can be chosen freely. The designed controller has a very simple structure and can be applied to track much broader classes of reference signals. It can guarantee the global boundness of all closed-loop signals and make the output tracking error arbitrarily small. Technique c) may provide the designer with the possibility to find a better choice of positive nonlinear functions for our controller to achieve similar tracking performance with less control effort.

Adaptive λ-tracking for a class of infinite-dimensional systems

For a class of high-gain stabilizable multivariable linear infinite-dimensional systems we present an adaptive control law which achieves approximate asymptotic tracking in the sense that the tracking error tends asymptotically to a ball centred at 0 and of arbitrary prescribed radius λ>0. This control strategy, called λ-tracking, combines proportional error feedback with a simple nonlinear adaptation of the feedback gain. It does not involve any parameter estimation algorithms, nor is it based on the internal model principle. The class of reference signals is W 1,∞, the Sobolev space of absolutely continuous functions which are bounded and have essentially bounded derivative. The control strategy is robust with respect to output measurement noise in W 1,∞ and bounded input disturbances. We apply our results to retarded systems and integrodifferential systems.

An Adaptive Servomechanism for a Class of Infinite-Dimensional Systems

A universal adaptive controller is constructed that achieves asymptotic tracking of a given class of reference signals and asymptotic rejection of a prescribed set of disturbance signals for a class of multivariable infinite-dimensional systems that are stabilizable by high-gain output feedback. The controller does not require an explicit identification of the system parameters or the injection of a probing signal. In contrast to most of the work in universal adaptive control, this paper is based on an input-output approach and the results do not require a state-space representation of the plant. The abstract input-output results are applied to retarded systems and integrodifferential systems.

Global output tracking for a class of single-input single-output non-linear systems

The problem of the global output tracking is considered for a class of single-input single-output systems. The class of non-linear systems considered here is constituted by the systems linearizable via state feedback, while the class of reference signals to be asymptotically tracked is constituted by the reference outputs generated by an external system: the exosystem. A procedure for the design of a compensator is proposed, which ensures a global convergence property, under a sufficient condition, which, in case of linear systems and of an exosystem constituted by a cascade connection of some integrators, reduces to the absence of invariant zeros in the origin of the complex plane. No minimum phase requirement is needed to apply the procedure. An example and some simulation runs are given showing the effectiveness of the proposed controller

Adaptive controllers and root loci of minimum-phase systems

We consider the class of multi-input, multi-output, finite-dimensional, minimum-phase systemsx=Ax+Bu,y=Cx, where it is required that det(CB) # 0, but the state dimension is unknown. For this class, a simple universal adaptive high-gain controller-not based on any identification mechanism-is introduced that ensures exponential decay to zero of the solution of the closed-loop system. Moreover, the terminal system is “almost always” exponentially stable. The switching-type controller switches between constant gains at discrete points of time and is based on the simple Willems-Byrnes controlleru(t)=−k(t)y(t), k(t) 2. The results are extended to solve the adaptive tracking problem for a certain class of reference signals.

On the Design of Servomechanisms via H 2 Optimization

Abstract The design of two-parameter controllers is considered for MIMO, linear plant-sensor systems. H2 optimization is used as a tool for selecting a controller amongst the ones which achieve closed-loop stability, asymptotic tracking of a class of reference signals, asymptotic rejection of disturbance signals. The cost functional takes into account the transient parts of the error and control signals. The original constrained problem is converted into an unconstrained one by means of an explicit parametrization obtained in a previous paper. Its solution is then given in quite explicit a form. Simple numerical examples are presented at the end

Robust adaptive control of plants with unknown order and high frequency gain

Abstract An adaptive control scheme is presented which has a simple structure and guarantees global stability of the closed-loop plant and asymptotic zero tracking error for a class of reference signals. The plants to be controlled are of minimum phase and relative degree one. No a priori knowledge for the order, the parameters of the plant or the sign of the high-frequency gain is required. The number of adjustable control parameters is proportional to the number of frequencies in the reference signal and is independent of the order of the plant. The proposed algorithm is then modified, by using a variable structure for generating the control signal, to guarantee robust stability of the closed-loop plant and asymptotic zero tracking error in the presence of bounded disturbances and unmodeled dynamics

Design of two-input one-output compensators to achieve asymptotic tracking

A procedure for designing two-input one-output compensators to achieve asymptotic tracking of a class of reference signals is presented. It is shown that if no mode of the reference signal is a transmission zero of the plant, the design is always possible. The design consists of two steps: stabilization and tracking.