Robust Tracking Problem Research Articles

Robust continuous-time tracking for multi-rate digital control systems

Rhe robust ripple-free tracking and regulation problem is solved for multi-rate sampled-data systems, whose state-space description depends on some unknown “physical” parameters. The used control system includes a periodic discrete-time subcompensator and, possibly, a continuous-time subcompensator. The conditions for the existence of a solution are found for two different convergence requirements: a prescribed rate of continuous-time exponential convergence of the error response and the free state response (to be obtained at least in a neighborhood of the nominal parameters), or a continuous-time dead-beat error and free state response at the nominal parameters (together with a continuous-time exponential convergence with any rate of convergence in some neighborhood of the nominal parameters). For both of them, the necessity of a wholly continuous-time internal model of the exogenous signals is proven, and a design procedure is proposed.

Decentralized output tracking of a class of nonlinear interconnected systems with similar structure via sliding mode technique

This paper addresses the robust output tracking problem for a class of non-linear interconnected systems with similar structure A robust decentralized control scheme for output tracking of a class of nonlinear interconnected system is proposed. It is shown that if uncertainties appear on system, the decentralized controller is able to perform approximate asymptotic tracking, in the sense that the output tracking error remains bounded, provided the upper bounds of the uncertain terms are known.

Robust stabilization of interval plants via an intelligent time-varying control scheme

The robust tracking problem for a family of linear uncertain plants is considered. The solution presented is in terms of a deterministic time-varying compensator, which may assume a finite number of possible different configurations, and of a supervisor. The task of the supervisor is that of determining the switching instants, and of a scanning among the elements of the family, according to a suitably defined experimental test on the tracking error. The switching scheme has been endowed with an intelligent adaptation mechanism, based on a performance index stopping the switching on the configuration corresponding to the model closest to the actual plant.

Robust output tracking of nonlinear systems with mismatched uncertainties

The problem of robust output tracking for a class of uncertain nonlinear systems which do not satisfy the conventional matching condition is considered. The main assumption on the uncertainty is that the triangularity condition is satisfied. Based on backstepping method and input/output linearization approach, we propose a class of non-adaptive state feedback controllers which can guarantee exponential stability of the tracking error for the uncertain nonlinear systems first. Next, adaptive control laws are developed so that no prior knowledge of the bounds on the uncertainties is required. By updating these upper bounds, we design a class of adaptive robust controllers. It is shown that under the proposed adaptive robust control the tracking error of the controlled system converges to zero as time approaches infinity.

Bezout factors and L/sup 1/-optimal controllers for delay systems using a two-parameter compensator scheme

The authors consider the simultaneous problem of optimal robust stabilization and optimal tracking for single-input/single-output (SISO) systems in an L/sup /spl infin//-setting using a two-parameter compensator scheme. Optimal robustness is linked to the work done by Georgiou and Smith (1992) in the L/sup 2/-setting. Optimal tracking involves the resolution of L/sup 1/-optimization problems. The authors consider in particular the robust control of delay systems. They determine explicit expressions of the Bezout factors for general delay systems which are in the Callier-Desoer class /spl Bscr//spl circ/(0). Finally, they solve several general L/sup 1/-optimization problems and give an algorithm to solve the optimal robust control problem for a large class of delay systems.

A Multivariable Two-Degree-Of-Freedom Control Methodology

This paper presents a two-degree-of-freedom design methodology based on a decoupling scheme. The proposed scheme is derived from the Youla parametrization and leads to a two-step design procedure. In the first step, a model-matching approach is proposed in order to set the desired nominal tracking objectives, while in the second step, μ-synthesis techniques are used in order to deal with the robust performance objectives. Special attention is paid to the robust tracking problem. For unstructured uncertainty, the most significant feature of the proposed design is that robust tracking requirements can be achieved, in a satisfactory way, by asimple H ∞ optimization. We carry out the design example on an ill-conditioned plant.

Multiple Objective Optimization Approach to Simultaneous Identification and Robust Adaptive Tracking

The problem of simultaneous optimal identification and robust tracking of uncertain linear systems on a finite time interval is formulated. An algorithm based on simultaneous state estimation and parameters identification and a certainty equivalence control algorithm is proposed. The main novelty of the presented approach is that the certainty equivalence control has, in addition of its control properties, qualities that are enhancing both the identification and robustness. Example is presented.

Robust output regulation for linear systems with structured uncertainty and with unmeasurable controlled output by high gain observer approach

This paper deals with the problem of robust tracking and disturbance rejection for a linear time-invariant system where the uncertainty of the system is represented in a structured form and the output to be controlled may be different from the measurement output. First, the problem is considered in a rather classical setting in that the required property of tracking and disturbance rejection can be attained as long as the resulting closed-loop system remains stable. Conditions for solvability of the problem are given and two algorithms are presented for designing controllers having the robust tracking and disturbance rejection property. Second, the problem of robust output regulation with robust stability is formulated as one of finding a controller such that the resulting closed-loop system satisfies an additional requirement of robust stability and thus the output regulation property can be maintained for all perturbations of uncertain parameters within a prescribed set. A procedure based on a high gain observer approach is proposed to solve this problem.

Adaptive Robust Control for Nonlinear Systems with Mismatched Uncertainties.

In this paper, the adaptive robust output tracking problem for a class of nonlinear systems which have both mismatched uncertainties and matched uncertainties has been addressed. The nominal system is input-output linearizable. Based on the input-output linearization technique and Lyapunov approach, an adaptive control law is developed to track the bounds on the plant uncertainties so that no prior knowledge of the bounds is required. it is shown that the output of the closed-loop systems ultimately track the desired output with a bounded tracking error despite the system uncertainties. An example is performed to illustrate the effectiveness of the proposed control scheme.

Robust time-optimal control of constrained linear Systems

A version of dynamic programming, which computes level sets of the value function rather than the value function set itself, is used to design robust non-linear controllers for linear, discrete-time, dynamical systems subject to hard constraints on controls and states. The controller stabilizes the system and steers all trajectories emanating in a prescribed set to a control invariant set in minimum time. For the robust regulator problem, the control invariant terminal set is a neighborhood, preferably small, of the origin; for the robust tracking problem, the control invariant terminal set is a neighborhood of the invariant set in which the tracking error is zero. Two non-linear controllers which utilize the level sets of the value function, are described. The first requires the controller to solve, on-line, a modest linear program whose dimension is approximately the same as that of the control variable. The second decomposes each level set into a set of simplices; a piecewise linear control law, affine in each simplex, is then constructed.

Asymptotic tracking in uncertain Volterra systems

This paper studies the robust tracking problem for an uncertain Volterra system via the frequency-domain approach. Based on the knowledge that the steady-state response of a Volterra system under the sinusoidal input contains possibly infinitely many frequency components, it is shown that (1) for any specified finitely many frequency components possibly contained in the steady-state tracking error, there exists a linear controller that robustly annihilates these components; and (2) robust tracking is possible by a linear controller provided that the Volterra system of the closed-loop system is polynomial. These results can be viewed as a nonlinear analog of the well-known linear robust servomechanism theory developed in the 1970s.

Augmented system approach to measurement-based robust tracking

This paper considers the robust tracking problem using an augmented system approach. Our results extend previous full-state results to observer-based feedback. The system matrix is assumed to contain time-invariant uncertainty. Two cases are considered. In the first, the tracked output is available for feedback. The resulting control law call be applied to polynomial reference signals of known order and results in zero steady-state error. In the second case, where the tracked output is not available for feedback, our approach is restricted to step references, and the steady-state error is non-zero, although bounded by a prescribed value.

Output tracking for linear uncertain time-delay systems

The paper considers the problem of robust output tracking of an uncertain system with multiple delays in both the state and control vectors. The disturbances are assumed constant, unknown but bounded. A robust output tracking scheme is proposed. The scheme guarantees asymptotic tracking of the command reference output, when the mismatched portion of the uncertainties satisfies a certain bound condition. In addition, the paper presents robust output tracking schemes for a class of matched uncertain time-delay systems and matched and mismatched uncertain nondelay systems. A numerical example is given to illustrate the results.

A minimal k-step delay controller for robust tracking of non-minimum phase systems

This paper considers the problem of look-ahead robust tracking for a non-minimum phase system under a sensitivity constraint. Because of non-minimum phase zeros, the exact tracking of arbitrary reference input is impossible. However, with an introduction of some delay, tracking is possible within any given “tolerance” ϵ 1 > 0. It is shown in the paper that the minimum delay required to satisfy the tracking performance is decoupled from a sensitivity/disturbance rejection constraint. Moreover, it is shown that calculation of the minimum delay reduces to a binary search problem.

Robust output regulation and tracking for linear periodic systems under structured uncertainties

The problem of robust output regulation and tracking is studied for a linear periodic discrete-time system whose state-space description depends on some unknown parameters. The preservation of asymptotic regulation and tracking under perturbations of such parameters is obtained for classes of exponential disturbance functions and reference signals. Both the conditions for the existence of a solution and a constructive design procedure for the periodic compensator are given.

Robust ripple-free regulation and tracking for parameter-dependent sampled-data systems

The robust ripple-free asymptotic tracking and disturbance rejection problem is studied for sampled-data systems whose matrices are assumed to depend on some "physical" parameters, each of which possibly affects all the elements of the matrices describing the system, and for the case when only a subset of the scalar outputs must track corresponding exogenous reference signals; ripple-free dead-beat regulation and tracking is also required at the nominal parameters. The necessary and sufficient conditions are given for the existence of a solution which may exist even when no solution exists for wholly independent variations of the entries of the matrices describing the system. A design procedure of both the continuous-time internal model and the discrete-time controller is also outlined.

Robustness Analysis of Sampled-Data Repetitive Control Systems

This paper formulates and analyzes a robust tracking problem for sampled data repetitive control systems in the presence of structured linear periodically time varying perturbations. Two pertinent issues are addressed. One is stability robustness, that is, if stability will be retained under such perturbations. The other is robust tracking, that is, if the tracking criterion will be met for all variations of the plant under the given class of perturbations. The tracking measure is taken to be the induced power-norm, which is defined as the power of the steady-state tracking error for the worst periodic input of unit power, and the tracking criterion is that only induced power-norms which are less than a prespecified bound are acceptable. A generalized notion of structured singular value, previously introduced in the literature. is used to answer these questions in the form of some necessary and sufficient conditions.

A robust H ∞ model reference tracking design for non-holonomic mechanical control systems

We propose a robust model reference tracking control design for non-holonomic mechanical systems under parametric perturbation and external disturbance. A design procedure with three-stage control is developed to solve the robust tracking problem for perturbative non-holonomic mechanical control systems. In the first stage, by a proper choice of transformation matrix, the perturbative non-holonomic mechanical system is transformed into a reduced form of non-holonomic mechanical system for the convenience of control design. In the second stage, based on the concept of ‘input/output decoupling’ in nonlinear control theory, a decoupled system with parameter perturbation and external disturbance is established via a nonlinear dynamic state feedback control. In the third stage, H ∞ criteria to specify desired model reference tracking performance in the face of parametric perturbation and external disturbance are proposed for the decoupled system. H ∞ controllers that achieve these H ∞ tracking performance ar...

Variable structure control with a second-order sliding condition: Application to a steam generator

A method for the design of second-order sliding mode controllers is developed for a class of nonlinear systems. The key idea is the necessity of nullifying both the auxiliary output as well as its time derivative when the system is sliding. It is found that if the auxiliary output has a strong vector relative degree one, it is possible to design a continuous control input. This allows the application of the sliding mode control to systems that do not allow discontinuous control signals generated by the classical variable structure control. Robustness of the controllers is analyzed and dynamic bounds for the uncertainty are found for a class of nonlinear systems. The design technique could be extended to nth-order sliding controllers, though the complexity of the calculations increases and the robustness bounds become more restrictive. The application of the technique to a drum-type steam generating unit to solve a robust tracking problem is presented.

Robust output tracking for nonlinear uncertain systems

The problem of robust output tracking for nonlinear systems in the presence of uncertainties is further studied by extending the results of Behtash (1990) to systems with mismatched uncertainties. A new design method which is called the Stable Combined Variable Perturbation Method (SCVPM) is proposed and a robust controller is presented using high-gain feedback. Our results are compatible with those of Behtash (1990) in a sense that the new controller will degenerate to the one of Behtash (1990) if the so-called generalized matching condition is satisfied. Simulation results verified the effectiveness of the newly proposed method and controller.