Unmodeled Uncertainties Research Articles

Bending and Torsional Vibration Control of a Flexible Structure Using H-infinity Based Robust Control.

This paper proposes a method for controlling the bending and torsional vibration of a flexible structure using Ha based optimal control. For this propose, we make a reduced order lumped mass model expressed by 3-DOF systems, considering the first three vibration modes and neglecting all the other high frequency modes. These neglected modes are regarded as unstructured uncertainties in the design stage. To prevent spillover instability caused by neglected mode, a modeling method based on the occurrence of uncontrollability and unobservability realized structurally at the nodes of the vibration modes is applied. Then, a static state feedback controller is designed based on the reduced order model and the approximate knowledge of the unmodeled uncertainties. The first three vibration modes of the flexible structure are controlled using a hybrid dynamic absorber. The discrete model and the controller design are verified through numerical simulations and experimental studies.

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.

Bending and Torsional Vibration Control of a Flexible Structure Using H-infinity Based Approach

This paper presents a method of controlling the bending and torsional vibration mode of a flexible structure using H-infinity optimal control. A new idea is proposed in order to reduce the unmodeled system uncertainties by placing actuators in the nodes of certain neglected vibration modes. Then, the controller is designed based on the reduced order model and is capable of attenuating vibration without causing spillover instability. For this purpose, a three degree of freedom lumped parameter mass model of a plate structure is considered to control its vibrations using a dynamic output feedback controller. The actuator dynamics and the placement of the actuators are considered for a effective controller design method. The efficacy of the controller is shown through simulations.

On the robust stability of a Clarke-Gawthrop type of self-tuning controller

In this paper the Clarke-Gawthrop type of self-tuning controller is modified and shown to be robust stable with respect to unmodelled plant uncertainties and bounded disturbances. A self-tuning controller is proposed here consisting of two steps: the first, an optimal control law, is derived by means of minimizing a quadratic cost function of the Clarke-Gawthrop type; the second, the optimal control law, is modified by introducing an estimate of the modelling error as a feedback. For the parameter estimation, a modified least-squares scheme with a relative dead zone is employed. The robustness results are derived by neither requiring too much a priori knowledge of the plant parameters, nor using any assumptions about the adaptive signals.

Design of dynamic dissipative compensators for flexible space structures

Control system design is considered for attitude control and vibration suppression of flexible space structures. The problem addressed is that of controlling both the zero-frequency rigid-body modes and the elastic modes. Model-based compensators, which employ observers tuned to the plant parameters, are first investigated. Such compensators are shown to generally exhibit high sensitivity to the knowledge of the parameters, especially the elastic mode frequencies. To overcome this problem, a class of dynamic dissipative compensators is next proposed which robustly stabilize the plant in the presence of unmodeled dynamics and parametric uncertainties. An analytical proof of robust stability is given, and a method of implementing the controller as a strictly proper compensator is described. Methods of designing such controllers to obtain optimal performance and robust stability are presented. Numerical and experimental results of application of the methods are presented, which indicate that dynamic dissipative controllers can simultaneously provide excellent performance and robustness. >

A Unified State-Space Solution to Unstructured Robustness and Disturbance Attenuation

In this paper, a unified framework for the robustness against various kinds of unmodelled uncertainty is presented. It is based on the H∞ optimization for a particular nominal feedback matrix. Within such a framework, disturbance attenuation is also considered. Furthermore, the more difficult problem, i.e., when there exists real parameter uncertainty for the plant, is studied.

Fault Detection via KDI in Presence of Unmodelled Uncertainty

Fault Detection via KDI in Presence of Unmodelled Uncertainty

Robust discrete time tracking control using sliding surfaces

This paper deals with the robustness issues associated with the feedforward tracking control with respect to unmodeled plant uncertainties. Based on the Diophantine equation, a new discrete time sliding functions has been defined and utilized for the robust feedforward tracking control law. The robustness is achieved by using a sliding function-based nonlinear feedback. As for model/plant mismatches the plant order uncertainty and parameter uncertainty are taken into account for robustness analysis. Noncircular machining has been adopted as an application example of this algorithm. Through computer simulation it has been shown that the robust discrete time tracking control is effective for unmodeled plant uncertainties.

Modeling with Respect to Uncertainties for a Magnetic Suspension System of a Double Flexible Beam

This paper describes a modeling with unmodeled uncertainties and control configuration for a magnetic suspension system of a double flexible beam. It simplifies both an elastic rotor and a body in a magnetic bearing system. At first, the magnetic suspension system is introduced. Next, dynamical equations of two beam motions as a concentrated state system and an electrical equation of an electromagnet are derived. Then its linearized model with disturbance terms as unmodeled uncertainties is formulated in a state space form. Finally, in order to deal with the uncertainties as a control problem, a standard H∞ control framework is set up. There the generalized plant is constructed from LQ differential game theoretical point of view, which involves weighting matrices for state variables and control input and frequency weighting functions for uncertainty models.

H.INF. Robust Control of a Magnetic Suspension System with Double Flexible Beam.

This paper describes H∞ robust control design for a magnetic suspension system of double flexible beam which simplifies both an elastic rotor and body in a magnetic bearing system. A magnetic bearing requires feedback control since it is inevitably unstable. Moreover, it is desirable that the controller guarantees robust stability at presence of a variety of uncertainties; errors of parameters, neglected nonlinearities, or unmodeled dynamics.At first, the magnetic suspension system is introduced. Next, its linearized model with disturbance terms as unmodeled uncertainties is formulated in a state space form. In order to deal with the uncertainties, the generalized plant is constructed from LQ differential game theoretic point of view, which involves weighting matrices for state variables and control input and frequency weighting functions for uncertainty models. Then the control systems are designed with both H∞ control and PID control, which are implemented by a digital controller using a digital signal processor. Finally, several experiments are made for the evaluation of the control performance, where the proposed control is compared with PID control.

Multi-objective controller design for discrete stochastic optimal systems with non-linear time-varying unmodelled dynamics and noise spectral uncertainties

A simple technique is introduced to synthesize an optimal controller, not only to minimize the least favourable cost functional J, but also to achieve the following purposes in discrete-time linear-quadratic-gaussian (LQG) optimal systems: (I) input-output decoupling; (2) stability robustness in the presence of non-linear time-varying (NLTV) unmodelled dynamics; (3) complete and arbitrary stable pole-placement; and (4) some zero-assignment, The Wiener-Hopi technique is employed and two weighting matrices Q(z) and R(z) of the quadratic cost functional are specified (by the inverse optimal control method), so that the controller is optimal with respect to the chosen weighting matrices and the design goals are achieved.