Class Of Multi-input Multi-output Nonlinear Systems Research Articles

Time-Scale Redesign-Based Saturated Controller Synthesis for a Class of MIMO Nonlinear Systems

A consideration of actuator saturation is an important aspect to study the effectiveness of a designed controller in practice. However, the conventional Lyapunov theory-based design is not always suitable to analyze the quantitative behavior of closed-loop system. This article presents a time-scale redesign-based saturated tracking controller for a class of feedback linearizable multi-input–multi-output (MIMO) nonlinear systems. The proposed controller is built upon the frameworks of contraction and partial contraction theories which ensures that bounded tracking performance as well as quantify the steady-state error bounds in terms of the various control design parameters. Notably, in contrast to the existing Lyapunov-method-based designs, the proposed approach allows to tune the controller performance without arbitrary reduction of singular perturbation parameters. Therefore, the vulnerability of the controller toward actuator saturation and noise, due to the ill-effects of high-gains stemming from the conventional high-gain controllers, are reduced. The extensive experimental results using a wheeled mobile robot are provided to demonstrate the effectiveness of the proposed controller.

Adaptive Fuzzy Actuator Failure Compensation Control for a Class of MIMO Nonlinear Systems

In this paper, an adaptive fuzzy control scheme is developed for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with uncertain actuator failures. Within this scheme, a fixed grouping of redundant actuators and a proportional actuation scheme for each group are considered. Afterward, a fuzzy system is used for the online approximation of a nominal control vector. The parameter adaptation laws for the nominal controller are driven by the prediction error, which is defined as the difference between the unknown nominal controller and the fuzzy controller. The proposed controller can compensate for both total and partial loss of effectiveness failure types. Closed-loop system stability and convergence properties of the tracking errors are proved based on Lyapunov theory. A piecewise analysis is carried out to prove that these properties hold despite the presence of parameter jumps caused by abrupt failures. A simulation study is carried out on a redundant joint two-link robot manipulator with joint failures at each link. Simulation results show the effectiveness of the proposed control scheme.

Global robust output regulation of a class of MIMO nonlinear systems by nonlinear internal model control

AbstractRecently, the global robust output regulation problem for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems which may not have well‐defined relative degree and are subject to a nonlinear exosystem has been studied based on a constructive nonlinear internal model. However, the proposed nonlinear internal model‐based control law is applicable to the case where the exogenous signals are reference input and/or measurable disturbance rather than unmeasurable disturbance. For this reason, this paper further studies the same control problem based on a general nonlinear internal model independent of the exogenous signal. It is shown that this control problem can be converted into a global robust stabilization problem of a more complicated MIMO nonlinear system with various uncertainties and well solved by a recursive state feedback controller design. Thus our approach applies to a broader class of output regulation problem of MIMO nonlinear systems.

Output-feedback adaptive control for a class of MIMO nonlinear systems with actuator and sensor faults

In this paper, an output-feedback adaptive control scheme is proposed for a class of multi-input multi-output (MIMO) nonlinear systems, aiming at tolerating unknown actuator faults and unknown sensor faults simultaneously. The number of actuator faults is allowed be infinity, while the sensors may suffer from bias and gain variation all the time. By constructing an auxiliary filter and estimating the bounds of the fault uncertainties, the effects of the faults are successfully compressed. Also, the difficulty related to the high-frequency gain matrix is circumvented by introducing a matrix factorization and a similarity transformation. The proposed scheme is able to ensure that all closed-loop signals are globally uniformly bounded and the tracking error converges to a residual set exponentially. Simulation results illustrate the effectiveness of the proposed scheme.

Passive actuator fault tolerant control for a class of MIMO nonlinear systems with uncertainties

ABSTRACTFault tolerant control of affine class of multi-input multi-output (MIMO) nonlinear systems has not received considerable attention of researchers compared to other class of nonlinear systems. Therefore, this paper proposes an adaptive passive fault tolerant control method for actuator faults of affine class of MIMO nonlinear systems with uncertainties using sliding mode control . The actuator fault is represented by a multiplicative factor of the control signal which reflects the loss of actuator effectiveness. The design of the controller is based on the assumption that the maximum loss level of the actuator effectiveness is known. Furthermore, since the proposed controller is adaptive, it does not require any a-priori knowledge of the uncertainty bounds. The closed-loop stability conditions of the controller are derived based on Lyapunov theory. The effectiveness of the proposed controller is demonstrated considering two examples: a two degree of freedom helicopter and a two-link robot manipulator and has been found to be satisfactory.

Nonlinear output regulation for invertible nonlinear MIMO systems

SummaryIn this paper, we address the problem of output regulation for a broad class of multi‐input multi‐output (MIMO) nonlinear systems. Specifically, we consider input–affine systems, which are invertible and input–output linearizable. This class includes, as a trivial special case, the class of MIMO systems which possess a well‐defined vector relative degree. It is shown that if a system in this class is strongly minimum phase, in a sense specified in the paper, the problem of output regulation can be solved via partial‐state feedback or via (dynamic) output feedback. The result substantially broadens the class of nonlinear MIMO systems for which the problem in question is known to be possible. Copyright © 2015 John Wiley & Sons, Ltd.

Adaptive actuator failure compensation control based on MMST grouping for a class of MIMO nonlinear systems with guaranteed transient performance

This paper presents a new adaptive compensation control approach for a class of multi-input multi-output (MIMO) nonlinear systems with actuator failures. In order to enlarge the set of compensable actuator failures, an actuators grouping scheme based on multiple model switching and tuning (MMST) is proposed for the nonlinear MIMO minimum-phase systems with multiple actuator failures. Then, an adaptive compensation scheme based on prescribed performance bound (PPB) which characterises the convergence rate and maximum overshoot of the tracking error is designed for the systems to ensure closed-loop signal boundedness and asymptotic output tracking despite unknown actuator failures. Simulation results are given to show the effectiveness of the control design.

Adaptive neural control for a class of MIMO nonlinear systems with extreme learning machine

This paper presents two adaptive neural control schemes for a class of uncertain continuous-time multi-input multi-output (MIMO) nonlinear dynamic systems. Within these schemes, the single-hidden layer feedforward networks (SLFNs) are applied to approximate the unknown nonlinear functions of the systems and then the neural controller is built based on the approximated neural models. The parameters of the SLFNs are modified using the recently proposed neural algorithm named extreme learning machine (ELM), where the parameters of the hidden nodes are assigned randomly. Different from the original ELM algorithm, the output weights are updated using the adaptive laws derived based on the Lyapunov stability theorem and Barbalat's lemma so that the asymptotical stability of the system can be guaranteed. The robustifying control term is also constructed to compensate for approximation errors of the SLFNs. In order to avoid the requirement of the approximation error bounds, the estimation laws derived based on the Lyapunov stability theorem and Barbalat's lemma are employed to estimate the error bounds in the second adaptive control scheme. Finally the proposed control schemes are applied to control a two-link robot manipulator. The simulation results demonstrate the effectiveness of the proposed control schemes for the MIMO nonlinear system.

Adaptive Output Tracking Control for a Class of MIMO Nonlinear Systems with Time-Delay

For a class of multi-input multi-output (MIMO) nonlinear system with time-delay, a problem of adaptive output tracking is investigated. Through applying the back-stepping recursive method, an adaptive output tracking controller is designed to achieve robust control. According to Lyapunov stability theory, Barbalat lemma, and Gronwall inequality, the designed state feedback controller not only guarantees the system states are uniformly bounded, but also ensures the system tracking error converges to a small neighborhood.

Improving Quality of Regulation of a Nonlinear MIMO Dynamic Plant

The paper presents a robust two-degrees of freedom control system for a multi-input, multi-output (MIMO) nonlinear dynamic process. There are discussed the advantages of the model following control (MFC) structure for MIMO systems, its stability and robustness properties and a method for synthesis of a multi-controller structure of the MFC model loop. The problems under study are exemplified by synthesis of a position and yaw angle control system for a 3DOF nonlinear mathematical model of a drillship, where the MFC structure is used to reduce effects of the impact of the sea current and wind forces on the ship's hull. perturbations, as well as great disturbances dumping at the input and at the output of the plant to be controlled (10)- (12). In the paper we fully utilize this theory and adopt the MFC advantages to synthesize a robust control system of improved quality for a class of nonlinear MIMO systems. The problems under study are exemplified by synthesis of a position and yaw angle control system for a drillship described by a 3DOF nonlinear mathematical model of low- frequency motions over the drilling point. The effectiveness of the proposed MFC structure is shown by its use to compensate the environmental disturbances, the impact of

Robust output regulation for a class of MIMO nonlinear systems with uncertain exosystems

The robust output regulation problem is considered for a class of multi-input multi-output (MIMO) nonlinear systems with uncertain exosystems. Under a mild assumption that the uncertainties of the controlled plant and exosystem have known boundary functions, a new design method of dynamic variable structure controller is proposed. It is proven that the tracking error of the closed-loop system can reach a specified manifold in a finite time and converge to zero asymptotically while all states involved are bounded. Simulation results of a permanent magnet synchronous motor servo system are given to validate the proposed approach.

Adaptive sliding mode control for a class of MIMO nonlinear systems with uncertainties

This paper proposes an adaptive scheme of designing sliding mode control (SMC) for affine class of multi-input multi-output (MIMO) nonlinear systems with uncertainty in the systems dynamics and control distribution gain. The proposed adaptive SMC does not require any a priori knowledge of the uncertainty bounds and therefore offers significant advantages over the non-adaptive schemes of SMC design. The closed loop stability conditions are derived based on Lyapunov theory. The effectiveness of the proposed approach is demonstrated via simulations considering an example of a two-link robot manipulator and has been found to be satisfactory.

Extended dynamic fuzzy logic system for a class of MIMO nonlinear systems and its application to robotic manipulators

SUMMARYThis paper presents an indirect adaptive fuzzy control scheme for a class of unknown multi-input multi-output (MIMO) nonlinear systems with external disturbances. Within this scheme, the dynamic fuzzy logic system (DFLS) is employed to identify the unknown nonlinear MIMO systems. The control law and parameter adaptation laws of DFLS are derived based on the Lyapunov synthesis approach. The control law is robustified in H∞ sense to attenuate external disturbance, model uncertainties, and fuzzy approximation errors. It is shown that under appropriate assumptions it guarantees the boundness of all signals in the closed-loop system and the asymptotic convergence to zero of tracking errors. An extensive simulation on the tracking control of a two-link rigid robotic manipulator verifies the effectiveness of the proposed algorithms.

Robust Adaptive Fuzzy Control by Backstepping for a Class of MIMO Nonlinear Systems

This paper presents a robust adaptive control method for a class of multi-input–multi-output (MIMO) nonlinear systems that are transformable to a parametric-strict-feedback form which has couplings among input channels and the appearance of parametric uncertainties in the input matrices. The proposed approach effectively combines the design techniques of robust adaptive control by backstepping and adaptive fuzzy-logic control in order to remove the matching-condition requirement and to provide boundedness of tracking errors, even under dominant model uncertainties and poor parameter adaptation. Unlike previous robust adaptive fuzzy controls of MIMO nonlinear systems, this research introduces the robustness terms explicitly in the controller structure to counteract the effects of model uncertainties and parameter-adaptation errors. Uniform boundedness of the MIMO nonlinear control system is proved, and simulation results further validate the effectiveness and performance of the proposed control method.

다입력 다출력 비선형 시스템의 관측기 설계 및 인덕션 모터에 응용

This paper presents an observer design method for a special class of multi input multi output(MIMO) nonlinear systems. First, we characterize the class of MIMO nonlinear systems with a block triangular structure. Also, the observability matrices for SISO nonlinear systems are extended to MIMO systems. By using the generalized observability matrices, it is shown that under the boundedness conditions of system state and input, the proposed observer guarantees the local exponential stability of error dynamics. Finally, its application to induction motor is given to verify the proposed method.

Decentralized-Like Adaptive Control for a Class of MIMO Nonlinear Systems

The design of stabilizing controllers for multi-input multi-output (MIMO) nonlinear plants with unknown nonlinearities is a challenging problem. The inability to identify the nonlinearities on-line or off-line accurately motivates the design of stabilizing controllers based on approximations or on approximate estimates of the plant nonlinearities. However, the design of centralized controllers for MIMO large-scale systems is complex due to the high dimensionality and difficulty of implementation in real time. In this paper, a decentralized-like nonlinear adaptive control algorithm is designed and analyzed for a class of MIMO large-scale nonlinear systems with unknown nonlinearities. In the control design each input is designed by assuming the effects of the other inputs is zero. The controller guarantees closed loop semi-global stability and convergence of the tracking error to a small residual set. The size of the residual set for the tracking error can be specified by choosing certain design parameters, which can be chosen to meet desired upper bounds for the tracking error.

Direct passivity of a class of MIMO non-linear systems using adaptive feedback

In this paper, an adaptive controller with adaptive laws specially designed is proposed to solve the problem of making a multi-input multi-output (MIMO) non-linear system, with explicit linear parametric uncertainty, equivalent to a passive system. These results are an extension of those obtained by the authors for the SISO case. Some stability issues associated to the resultant closed-loop passive system are also discussed. The results obtained are applied to models of dynamical MIMO systems, to illustrate the controller design methodology.