Effects Of Unmodeled Dynamics Research Articles

Robust fault detection based on compensation of the modelling error

The problem of compensation of modelling errors for the purpose of robust fault detection based on parity relations is addressed. The idea is to approximate unmodelled non-linear dynamics by a neural network model and then to remove the effects of unmodelled dynamics from the primary residuals. The design of such a compensator takes two steps. In the first, a subset of the most informative regressors is selected. The second step entails structure determination and parameter estimation by means of numerical optimization of a criterion function. The criterion reflects a compromise between the quality of approximation and the complexity of the model structure. The results from the study on a three-tank test rig are presented and a comparison between compensated and uncompensated residuals made. It is shown that the compensated residuals represent a good basis for reliable, yet sensitive enough, fault detection and isolation.

Robust feedback control of combustion instability with modeling uncertainty

This paper presents the design of a robust feedback controller for suppressing combustion instabilities in propulsion systems with distributed actuators. The control synthesis procedure is based on the H ∞-optimization, which guarantees robust stability and performance within specified uncertainty bounds by taking into account the effects of unmodeled dynamics, sensor noise, and parametric errors. It makes use of an observer structure for robust estimation of combustion dynamics, and an H ∞ loop-shaping for performance requirements. Results of simulation experiments are presented to show how longitudinal pressure oscillations can be suppressed in a generic combustion chamber. The closed-loop control system exhibits robust stability and performance in the presence of exogenous disturbances and parametric errors.

On robustness in system identification

This paper studies robustness issues in system identification. Specifically, a general framework for robust convergence analysis is given for identification of stable linear time-invariant systems. This is used to derive a rather complete set of results on robust convergence under average l p norms, Orlicz norms, and cross-correlation-type noise semi-norms. The new theory is used to discuss and to study robustness issues in identification of linear time-invariant models when the true plant is not exactly linear. Robustness issues in system identification against unmodelled nonlinear dynamics are important, as real plants exhibit typically at best nearly linear dynamics. The results show clearly that the effects of unmodelled dynamics are typically more serious than those of random noise.

A decentralized indirect adaptive control for a class of two-time-scale nonlinear systems with application to flexible-joint manipulators

In this paper, the problem of an indirect adaptive decentralized control for a class of two-time scale interconnected systems is considered. The concept of an integral manifold is first utilized to construct the dynamics of corrected slow subsystems. Fast subsystems are also constructed to represent the dynamics of the fast modes. A composite control scheme based on full state feedback is then developed to guarantee stability and robustness of the closed-loop system. The controller is designed by taking into account the effects of unmodeled dynamics, identification errors, and parameter variations. Stability analysis of the resulting closed-loop full-order system subject to the composite controller is presented. To demonstrate the application of the proposed algorithm, an example of a two-link flexible-joint manipulator is considered. Simulation results are provided to validate the applicability of the proposed control scheme.

Controlling nonlinear time-varying systems via euler approximations

A discrete time model reference control algorithm for continuous time systems represented by essentially unknown nonlinear time-varying ordinary differential equations is presented and analysed. Provided the reference model and the inverse dynamics of the plant are bounded input bounded output stable it is shown that a discrete control using state measurements based on Euler approximations for the systems response can achieve arbitrary tracking accuracy. The effect of unmodelled dynamics and disturbances is analysed.

Model Reference Adaptive Control and Adaptive Stability Augmentation

Abstract A comparison of the standard concepts in MRAC design suggests that a combination of the implicit and the explicit design techniques may lead to an improvement of the overall system performance in the presence of unmodelled dynamics. Using the ideas of adaptive stability augmentation a combined stability augmented model reference design is proposed. By utilizing the closed-loop control error, a simple auxiliary controller is tuned, using a normalized M.I.T. rule for the parameter adjustment. The M.I.T. adjustment is protected against the effects of unmodelled dynamics by lowpass filtering of the gradient. The proposed method is verified through simulation results indicating that the method may lead to an improvement of the model reference controller in the presence of unmodelled dynamics.

Hard frequency-domain model error bounds from least-squares like identification techniques

The problem of deriving so-called hard-error bounds for estimated transfer functions is addressed. A hard bound is one that is sure to be satisfied, i.e. the true system Nyquist plot will be confined with certainty to a given region, provided that the underlying assumptions are satisfied. By blending a priori knowledge and information obtained from measured data, it is shown how the uncertainty of transfer function estimates can be quantified. The emphasis is on errors due to model mismatch. The effects of unmodeled dynamics can be considered as bounded disturbances. Hence, techniques from set membership identification can be applied to this problem. The approach taken corresponds to weighted least-squares estimation, and provides hard frequency-domain transfer function error bounds. The main assumptions used in the current contribution are: that the measurement errors are bounded, that the true system is indeed linear with a certain degree of stability, and that there is some knowledge about the shape of the true frequency response. >

Robust adaptive control of a class of nonlinear mechanical systems with unbounded and fast-varying uncertainties

The class of system addressed in this paper consists of multibody mechanisms with open or closed kinematic chains. The constraints imposed by interbody connections are holonomic and scleronomic. Uncertainties result from unknown system parameters, external disturbances and some unmodeled dynamic effects. The plant model, available for a controller, represents only a few very general properties of multibody dynamic systems. The coefficients and terms of the plant equation may be potentially unbounded and fast varying. Such a general model includes a large class of unmodeled dynamics and any bounded external disturbances. Novel adaptive and control laws are presented. The stability and robustness analysis, performed by the Lyapunov method, has proven that the proposed controller keeps the tracking errors within a certain computable tolerance. As a particular case of the general theory, the tracking control of robotic manipulators has been discussed in detail.

Minimax model reference adaptive control for a plant subject to unmodeled dynamics

Abstract It is well‐known that a real system is always subject to the impact of unmodeled dynamics. In this paper, a cost function of weighting output error (i.e., the difference between the reference model output and the plant output) and control input is minimized by the theory of minimax optimization to reduce the effect of unmodeled dynamics. Furthermore, the stability and robustness of an adaptive controller are achieved by the utilization of a modified dead‐zone least‐squares parameter estimator with non‐vanishing gain matrices, and the constraint of plant parameter in a finite set of convex sets. The choice of the size of the dead zone and its effect on tracking error are also discussed.

Indirect adaptive techniques for fixed controller performance enhancement

Abstract This paper develops the adaptive disturbance estimate feedback schemes of a companion paper for enhancing the performance of controllers designed by off-line techniques. The developments are based on the parametrization theory for the class of all stabilizing controllers for a nominal plant, and the dual class of plants stabilized by a nominal controller. Such parametrization allows us conveniently to parametrize plant uncertainties for on-line identification and control purposes, minimizing the effects of unmodelled dynamics. Based on these parametrizations, along with prefiltering which minimizes the effect of unmodelled dynamics, standard adaptive stabilization, adaptive pole assignment, or adaptive linear quadratic schemes are shown to achieve controller enhancement. The idea is to exploit a priori information about a plant and design objectives in an off-line design, and yet exploit the power of adaptive techniques to learn and tune on-line. Attention is focused on techniques for fixed but u...

Bifurcation in model reference adaptive control systems

We study the effect of unmodeled dynamics on the performance of a simple model reference adaptive control mechanism. Exact stability boundaries are computed and different routes to chaotic behavior and global instability are described. Typically, we observed a region of period doubling and Hopf bifurcations similar to those observed in the Ziegler-Nichols approach to PID control design. The analysis applies to higher order and certain nonlinear systems as well.

Singular Perturbation Techniques in the Adaptive Control of Elastic Robots

The problem of controlling robots with rotary flexible joints is considered. If the amount of flexibility at joints is small the model is shown to be singularly perturbed. This allow us to evaluate the effect of unmodeled dynamics when control designed under the assumption of stiff joints are employed; in this case also diverging oscillations can arise. Moreover the singular perturbation formulation suggests the use of a composite feedback control, that is a fast feedback control is added to a slow control designed on the basis of the dynamics of the stiff corrispondent robot.

A Frequency Domain Analysis of Direct Adaptive Pole Placement Algorithms in the Presence of Unmodelled Dynamics

This paper examines a general class of direct adaptive pole placement algorithms in the presence of unmodelled high frequency dynamics. The analysis is broken into three stages. The first stage addresses the robustness of the fixed control structure on which most continuous time adaptive control schemes are based. The second stage looks at the effect of unmodelled dynamics on the estimation model used in equation error formulations of continuous time algorithms. The last stage looks specifically at the identification process.