Presence Of Unmatched Uncertainties Research Articles

Sliding mode control of a two-link flexible manipulator for reduced vibration in the presence of unmatched uncertainty and time-varying external disturbance

Sliding mode control of a two-link flexible manipulator for reduced vibration in the presence of unmatched uncertainty and time-varying external disturbance

Sliding mode control of Two-link Flexible Manipulator for reduced vibration in the presence of unmatched uncertainty and time-varying external disturbance

Sliding mode control of Two-link Flexible Manipulator for reduced vibration in the presence of unmatched uncertainty and time-varying external disturbance

Valid RBFNN Adaptive Control for Nonlinear Systems With Unmatched Uncertainties.

In this article, an adaptive tracking controller based on radial basis function neural networks (RBFNNs) is proposed for nonlinear plants with unmatched uncertainties and smooth reference signals. The concept of valid RBFNN adaptive control is introduced where all closed-loop arguments of the involved RBFNNs should always remain inside their corresponding compact sets. Considering the local approximation capacity of RBFNNs, validity requirements are necessary for ensuring reliable closed-loop approximation accuracy and stability. To obtain valid RBFNN adaptive controllers, a novel iterative design method is proposed and embedded into the traditional backstepping approach. In the initial iteration, an ideal RBFNN and its online estimated version are introduced in each step where the initial compact set guarantees the validity requirement for only a finite time interval. Then, by carefully investigating the dependence among different signals and introducing some auxiliary variables, the compact sets are redesigned for prolonging the time interval satisfying validity requirements to infinity as the iteration goes on. Consequently, a closed-loop system model can be formulated during the entire control process, which underlies a rigorous proof on closed-loop stability and some guidelines on practical implementation. Meanwhile, rigorous analysis from validity requirements reveals, for the first time, a new feature of RBFNN adaptive controllers in the presence of unmatched uncertainties: excessively large scales of RBFNNs in intermediate steps may impair the closed-loop performance. Finally, simulation results are provided to illustrate the efficiency and feasibility of the obtained results.

Parameter Convergence in Adaptive Control in Presence of Unmatched Uncertainty

The problem of convergence of uncertainties to their true values is of great interest in adaptive control. It is desirable as it facilitates accurate online modeling of structured uncertainties and robust adaptation to disturbances. The adaptation law based on the classical gradient method requires the restrictive persistent excitation (PE) condition to be satisfied for parameter convergence. This paper deals with the relaxation of this PE condition for a class of nonlinear systems in the presence of unmatched uncertainty. The design of the proposed adaptive backstepping controller involves multiple filtered models that translate the restrictive PE condition to linear independence of the filtered regressor models. The proposed controller guarantees asymptotic convergence of the tracking and parameter estimation errors globally in the presence of unmatched uncertainty. Numerical simulations show the efficacy of the proposed controller.

Finite-time terminal synergetic control of a class of nonlinear systems with unmatched uncertainties

Abstract In this paper, the problem of finite-time tracking for nth-order uncertain nonlinear systems with unmatched uncertainties is addressed. Using a terminal synergetic manifold, a controller is provided to force the tracking error to the origin in finite time in the presence of unmatched uncertainties. With this method, chattering problem is completely removed without defining a new function. Lyapunov theory is used to prove the stability of the proposed method. The proposed controller provides the convergence of finite-time tracking error to zero by suitable performance that is theoretically analysed and proved through simulation.

Discrete‐time higher‐order sliding mode control of systems with unmatched uncertainty

SummaryThe research on discrete‐time higher‐order sliding mode has received a considerable attention recently. Systems with unmatched uncertainties are common in practice; however, the existing discrete‐time higher‐order sliding mode control algorithms are designed considering only matched uncertainty. This paper proposes a technique to design discrete‐time higher‐order sliding mode control for an uncertain LTI system in the presence of unmatched uncertainty. The proposed technique is numerically simulated and experimentally validated on an electromechanical rectilinear plant. Various experiments are conducted considering the several operational conditions of electromechanical systems in industries to verify the performance of the proposed controller.

Combined Speed and Current Terminal Sliding Mode Control With Nonlinear Disturbance Observer for PMSM Drive

A terminal sliding mode control (SMC) method based on nonlinear disturbance observer is investigated to realize the speed and the current tracking control for the permanent magnet synchronous motor (PMSM) drive system in this paper. The proposed method adopts the speed-current single-loop control structure instead of the traditional cascade control in the vector control of the PMSM. First, considering the nonlinear and the coupling characteristic, a single-loop terminal sliding mode controller is designed for PMSM drive system through feedback linearization technology. This method can make the motor speed and current reach the reference value in finite time, which can realize the fast transient response. Although the SMC is less sensitive to parameter uncertainties and external disturbance, it may produce a large switching gain, which may cause the undesired chattering. Meanwhile, the SMC cannot keep the property of invariance in the presence of unmatched uncertainties. Then, a nonlinear disturbance observer is proposed to the estimate the lump disturbance, which is used in the feed-forward compensation control. Thus, a composite control scheme is developed for the PMSM drive system. The results show that the motor control system based on the proposed method has good speed and current tracking performance and strong robustness.

L1 adaptive controller of nonlinear reference system in presence of unmatched uncertainties

An extension of L1 adaptive control is proposed for the unmatched uncertain nonlinear system with the nonlinear reference system that defines the performance specifications. The control law adapts fast and tracks the reference system with the guaranteed robustness and transient performance in the presence of unmatched uncertainties. The interval analysis is used to build the quasi-linear parameter-varying model of unmatched nonlinear system, and the robust stability of the proposed controller is addressed by sum of squares programming. The transient performance analysis shows that within the limit of hardware a large adaption gain can improve the asymptotic tracking performance. Simulation results are provided to demonstrate the theoretical findings of the proposed controller.

Residual generation with unknown input observer for linear systems in the presence of unmatched uncertainties

In this paper, we deal with residual vector generation for fault detection problems in linear systems via unknown input observer (UIO) when the so-called observer matching condition is not satisfied. Based on the relative degree between unknown input and output, a vector of the auxiliary output is introduced so that the observer matching condition is satisfied with respect to the vector. Auxiliary outputs are related to the derivatives of measured signals. However, differentiation leads to excessive amplification of measurement noise. A dynamically equivalent configuration of linear systems is developed using successive integrations to avoid differentiation. As such, auxiliary outputs are constructed without differentiation. Then, the equivalent dynamic system and its corresponding auxiliary outputs are used to generate the residual vector via an exponentially converging UIO. Fault detection in the generated residual vector is also investigated. Finally, the effectiveness of the proposed method is shown via numerical simulation.

A SWITCHING SCHEME FOR THE ROBUST STABILIZATION OF DISCRETE TIME SYSTEMS WITH UNMATCHED UNCERTAINTIES

In this paper robust control of discrete time linear systems in presence of unmatched uncertainties is considered. Discrete time Variable Structure Control is used, and the presence of the sector, always affecting this control approach, is avoided by means of Switching Control. This latter is based on a suitable partition of the parameter space, while each single controller is based on Discrete time Variable Structure Control. It is worth noticing that the proposed approach does not depend on the duration of the sampling interval, hence it works both for sampled data system and for “pure” discrete time systems.

Sliding mode controller-observer systems with unmatched uncertainty

This paper presents sufficient conditions for the sliding mode control of a system with disturbance input. The behaviour of the sliding dynamics and a method for the design of asymptotically stable sliding observers for linear multivariable systems are studied. The sliding observer design ensures that, in the presence of unmatched uncertainty, the estimated state nearly approaches the actual state. Certain sufficient conditions should be satisfied for the asymptotic stability of the error system.

A nonlinear control strategy for robust sliding mode performance in the presence of unmatched uncertainty

It is well known that sliding mode control schemes provide robustness to the class of uncertainty acting within channels implicit in the control inputs: the so-called matched uncertainty. However, the unmatched uncertainty will affect the ideal dynamics prescribed by the chosen switching surfaces. This paper develops a control strategy to minimize the effects of the unmatched uncertainty upon the dynamic performance prescribed by the switching surfaces. This is achieved for a subclass of the uncertainty class considered by previous authors. The practical application of the control strategy to the design of a stability augmentation system for a light aircraft is presented. For this problem an ideal performance is well known and it is desirable that these ideal dynamics are exhibited across a wide range of flight conditions without degradation.

Choice of discontinuous control component for robust sliding mode performance

Abstract The robustness properties of sliding mode behaviour are considered in terms of the choice of non-linear control structure. The performance of two classes of variable structure controllers in the presence of unmatched uncertainty is discussed. Criteria for suitable choice of a non-linear control structure are presented, and the concept of a performance sliding mode is introduced. A numerical example is given to illustrate the phenomenon described