Class Of MIMO Nonlinear Systems Research Articles

Command Filtered Event-Triggered Adaptive Control for a Class of MIMO Nonlinear Systems Based on Neural Network Model

Command Filtered Event-Triggered Adaptive Control for a Class of MIMO Nonlinear Systems Based on Neural Network Model

Stabilization Problem for a Class of Nonlinear MIMO Systems Based on Prescribed-Time Sliding Mode Control

Stabilization Problem for a Class of Nonlinear MIMO Systems Based on Prescribed-Time Sliding Mode Control

Nonlinear disturbance observer-based adaptive nonlinear model predictive control design for a class of nonlinear MIMO system

Model predictive control with less prior knowledge of system uncertainty and external disturbance is a long-standing theoretical and practical problem. In this paper, a solution is presented by proposing a disturbance observer-based adaptive nonlinear model predictive control scheme for a class of nonlinear MIMO systems. Our scheme requires the state and parameterdependent state-space model to linearise the nonlinear system along the prediction horizon. To cope with the unknown system uncertainty, the multiple estimation model and the concept of second-level adaptation [Pandey, V. K., Kar, I., & Mahanta, C. (2014). Multiple models and second level adaptation for a class of nonlinear systems with nonlinear parameterisation. In Industrial and Information Systems (ICIIS), 2014 9th International Conference on (pp. 1–6). IEEE.] technique for the nonlinear system is used. To ensure the boundedness of the estimated parameter, a projection-based adaptive law [Hovakimyan, N., & Cao, C. (2010). L1 adaptive control theory: Guaranteed robustness with fast adaptation. SIAM.] is used. Using a twin-rotor MIMO system (TRMS), the effectiveness of the proposed control algorithm has been verified. Simulation and real-time results show that the proposed control algorithm performs better than the existing control algorithm in the presence of unknown external disturbance and parameter uncertainties.

Nonlinear disturbance observer‐based adaptive feedback linearized model predictive controller design for a class of nonlinear systems

AbstractAdaptive control with less prior information of a nonlinear system subjected to external disturbance and parametric uncertainties is a longstanding problem in the control community. In this paper, a nonlinear disturbance observer‐based adaptive feedback linearized model predictive control (NDO‐AFLMPC) technique is proposed for a class of nonlinear MIMO systems. In this approach, a nonlinear disturbance observer (NDO) is used to observe the external disturbance of the system. A suitable constraint mapping algorithm is developed to map the input–output constraints within the proposed control scheme. Here, a multiple estimation model and the concept of second‐level adaptation technique is used to handle the parametric uncertainty of the real‐time plant. The boundedness of the estimated parameter is solved by developing the projection‐based parameter adaptation laws. Using an aerodynamic laboratory set‐up, known as the twin‐rotor MIMO system (TRMS), the effectiveness of the proposed control algorithm is verified. The complete state information of the real‐time system is provided to the proposed adaptive controller from an extended Kalman filter (EKF)‐based state observer. The performance of the proposed control algorithm is compared with other existing nonlinear control algorithms in the presence of unknown external disturbance and parametric uncertainties.

Extended prescribed performance control with input quantization for nonlinear systems

AbstractFor a class of MIMO nonlinear systems, comprised of interconnected subsystems in Brunovsky canonical form, with uncertain yet locally Lipschitz nonlinearities among subsystems and quantized inputs, the target is to form a closed‐loop system that exhibits extended prescribed performance on states tracking (accuracy determined by maximum overshoot, minimum convergence rate, maximum steady‐state error, and control gains), yet still a low‐complexity control structure, without requiring any identification, approximation, and filtering techniques, regardless of uncertainties. In this article, a static, decentralized, continuous, yet computationally inexpensive controller is designed, without requiring parameters of quantizers. Inheriting the merit of pioneering prescribed performance control (PPC) methodology, it is required that the reference signal is function only, while, an essential difference and new feature is that, the pioneering PPC guarantees that state tracking errors are constrained by boundary functions (also known as prescribed performance functions, PPFs) only, while, the proposed extend PPC scheme achieves that state tracking errors are constrained by boundary functions and control gains simultaneously, in other words, without “tighter” PPFs, state tracking errors can still be adjusted to arbitrarily small by choosing proper control gains. Finally, comparative simulation results are given to verify the theoretical findings.

Robust Passivity-based Sliding Mode Control of a Large Class of Nonlinear Systems Subject to Unmatched Uncertainties: A Robot Manipulator Case Study

The existence of unmatched uncertainties is known as a serious challenge for designing a robust sliding mode control (SMC) law for nonlinear systems. To pass over this obstacle, a novel robust passivity-based sliding mode approach is proposed here for a large class of MIMO nonlinear systems. The design procedure is accomplished in two steps in presence of both matched and unmatched uncertainties. First, an efficient adaptive sliding surface is designed based on the passivity concept. The passivity provides a flexible robust structure for the sliding surface and guarantees the global asymptotic stability of the reduced-order equations of the system as well. Furthermore, simple adaptation laws are obtained to eliminate the effects of uncertainties. Then, the robust controller is formulated using the SMC method. As another important advantage, the proposed approach is relaxed from the upper bound’s constraints of the uncertainties. It is also applied to n-link rigid electrically driven robot manipulator as a widely-used practical nonlinear system. The simulation results show the appropriate tracking performance for the industrial selective compliance assembly robot arm (SCARA) in the presence of noisy external disturbances. Also, an extending case is studied with related research to emphasize the potential of the proposed approach.

A New Adaptive Explicit Nonlinear Model Predictive Control Design for a Nonlinear MIMO System: An Application to Twin Rotor MIMO System

This paper proposed an adaptive explicit nonlinear model predictive control (AENMPC) technique using multiple estimation models with a convex combination framework [18] for a class of nonlinear MIMO systems. Here, the explicit solution for the control signal is obtained from an optimal performance index which can be formulated without online optimization. In this work, a closed-form control law is developed by approximating the tracking error in the receding horizon by its Taylor series expansion. The control performance of any model-based control technologies explicitly depends on the quality of the unknown system parameters hence an adaptive parameter estimator is used to estimate the system parameter online [16,17]. To ensure the boundedness of the estimated parameter within a predefined compact region, a projection based adaptive law is used [43]. Using an aerodynamic laboratory set-up, known as the twin-rotor multi-input multi-output system (TRMS), the effectiveness of the proposed control algorithm has been verified. The complete state information of the system to the proposed adaptive controller is given from an extended Kalman filter based state observer. The performance of the proposed adaptive control algorithm has been verified successfully in simulations as well as real-time experimental setup of the TRMS model and compared with an existing control approach.

Continuous sliding mode iterative learning control for output constrained MIMO nonlinear systems

This paper investigates the time-varying output constraints tracking problem for a class of MIMO nonlinear system, where a new design of Iterative Learning Control (ILC) with adaptive sliding mode method is implemented. Firstly, to solve the unknown periodic parameters problem of MIMO nonlinear system, an ILC strategy is applied to estimate the parameters values which are difficult to be obtained accurately. Secondly, in view of unknown bounded disturbances, a continuous second-order sliding mode adaptive algorithm is utilized, where the disturbances can be estimated by the adaptive law without the upper bound knowledge. Meanwhile, the second-order sliding mode integral term is employed to suppress chattering phenomena. Then, considering the prescribed tracking performance, a novel universal Barrier Lyapunov Function (BLF) is proposed to address the constraint requirements which can change along with the time domain and the iteration domain. The stability and iterative convergence of the adaptive iterative learning sliding mode controller with time-varying constraints are proved by composite energy function (CEF). Finally, the effectiveness of the proposed algorithm is verified by simulation results.

LMI-based robust tracking of a class of MIMO nonlinear systems

Reference tracking problem for MIMO Lipschitz nonlinear systems is examined here. Presently a vast literature exists on observer design of unforced systems containing Lipschitz nonlinearities. However, these existing results cannot be readily extended for controller design containing reference tracking ability. Here a Linear State Variable Feedback (LSVF) controller is designed for MIMO Lipschitz nonlinear systems with norm-bounded parametric uncertainties using the concept of input to state stability Lyapunov functions. The whole problem is cast into a framework of Linear Matrix Inequalities, to exploit its numerical capabilities. Analytical proofs are supplemented with simulation examples, which show certain advantages over existing results. Apart from state feedback, observer-based output feedback is also considered for controller design.

T‐S modelling‐based anti‐disturbance finite‐time control with input saturation

Here, the problem of finite-time disturbance rejection is investigated for a class of MIMO non-linear systems with both unknown external disturbances and actuator saturation in the disturbance-observer-based control (DOBC) framework. In order to expand the application range of external disturbances, Takagi-Sugeno (T-S) fuzzy model is used to describe the complex non-linear disturbance. By constructing an appropriate Lyapunov function, an observer-based controller is designed to guarantee that the closed-loop system is finite-time stable. Finally, a simulation example for A4D flight control systems with non-linear disturbances is given to demonstrate the effectiveness of the proposed approach.

Design of sliding mode control for quadruple-tank MIMO process with time delay compensation

In industrial applications, process delay and disturbance are considered to be major concerns which are responsible for the deterioration in the performance of multivariable systems. quadruple tank process (QTP) is one of the multivariable system that requires control over at least two variables. This paper deals with the designing of robust control strategy for quadruple-tank MIMO process with time delay compensation in the presence of matched uncertainty and process delays. The Sliding Mode Control (SMC) is designed for the class of non-linear MIMO system. The process delays in the system are compensated using Pade Approximation technique. The sliding mode control law is derived using non-switching reaching law which provides faster convergence speed for states and negligible chattering at the control signal. The sufficient condition for closed-loop stability of MIMO system is derived using Lyapunov approach. Simulation study focuses on a MIMO quadruple-tank process having process delays and matched disturbances. Simulation results are presented and compared with conventional quadruple tank process having process delays and power-rate reaching law to show the effectiveness of time delay compensation and robustness of proposed control algorithm derived using non-switching type reaching law in the presence of matched uncertainties and process delays.

Observer-based adaptive fuzzy tracking control for a class of MIMO nonlinear systems with unknown dead zones and time-varying delays

ABSTRACTThe adaptive tracking control strategy is investigated for a class of multi-input and multi-output pure-feedback nonlinear delayed systems with unknown dead-zone inputs. This problem is challenging due to the existence of unknown dead zones, time-varying delays and unavoidable state variables. By constructing fuzzy approximators and state observers, the difficulties from unknown nonlinearities and unavailable state variables are surmounted, respectively. Lyapunov–Krasovskii functions are introduced to deal with the time-varying delays. The adaptive controllers are designed by a backstepping method and adaptive technique so that the closed-loop systems remain stable and the target signals can be tracked within a small error as well. At last, two examples are provided to show the effectiveness of the proposed scheme.

A novel adaptive non-backstepping VUFC algorithm for a class of MIMO nonlinear systems with unknown dead-zones in pure-feedback form

In this paper, based on adaptive non-backstepping design algorithm, we proposed a novel variable universe fuzzy control (VUFC) algorithm for a class of MIMO nonlinear systems with unknown dead-zone inputs in pure-feedback form. First, by introducing some new states variables and coordinate transforms, the system is converted form the state-feedback control of pure-feedback form into the output-feedback control of normal form. Secondly, different from traditional backstepping scheme,we introduce contraction–expansion factors, combine non-backstepping control technique and VUFC scheme together to construct the controllers and observers. VUFC approach is mainly based on changing the contraction–expansion factor to change the universe of the variables (which can change the interpolation node encryption). It is shown that the proposed control approach is considerably simpler and better than the backstepping-based ones and it can improve the accuracy of the system, alleviate tracking error, strong robustness. At last, according to stable positive real (SPR)-Lyapunov stability analysis, it can guarantee that all the signals in the closed-loop system are bounded and the output can tack the reference signal to a small neighborhood of the origin. Simulations results are illustrated that the effectiveness of the proposed VUFC approach.

A robust direct adaptive fuzzy control for a class of uncertain nonlinear MIMO systems

A robust direct adaptive fuzzy controller for a class of MIMO nonlinear systems with uncertainties and external disturbances is presented. The robust adaptive fuzzy controller is successfully employed using tracking error universe. Also adaption laws of the proposed controller are developed such that to be guaranteed the steady constant of the adjustable parameters and the estimated bound of the uncertainties and approximation error without utilizing any modification algorithm. Stability of the proposed method, i.e., uniformly ultimately boundedness of the tracking error and all involved signals, is shown based on Lyapunov theory. Simulation results demonstrate the capability and efficiency of the proposed technique for controlling nonlinear systems with uncertainties and external disturbances.

Adaptive tracking for MIMO nonlinear systems with Unknown fast time‐varying parameters

SummaryIn this paper, we consider a class of MIMO nonlinear systems with fast time‐varying parametric uncertainties. First, the tracking problem of general nonlinearly time‐varyingly parameterized systems is solved. Then, a Lyapunov‐based singularity free adaptive controller is proposed for the considered system. Specifically, an estimation approach with a proportional plus integral adaptation scheme is utilized to update the estimations of the unknown parameters under a mild assumption that the signs of the leading minors of the input gain matrix are known. The asymptotic stability is achieved with full state feedback. Furthermore, we design an output feedback controller by utilizing a standard high‐gain observer and achieve uniformly ultimately bounded convergence. Simulation examples illustrate the effectiveness of the proposed methods.

Approximate decoupling and output tracking for MIMO nonlinear systems with mismatched uncertainties via ADRC approach

In this paper, we consider output tracking for a class of MIMO nonlinear systems which are composed of coupled subsystems with vast mismatched uncertainties. First, all uncertainties influencing the performance of controlled outputs, which include internal unmodelled dynamics, external disturbances, and uncertain nonlinear interactions between subsystems, are refined into the total disturbance in the control channels of subsystems. The total disturbance is shown to be sufficiently reflected in the measured output of each subsystem so that it can be estimated in real time by an extended state observer (ESO) in terms of the measured outputs. Second, we decouple approximately the MIMO systems by cancelling the total disturbance based on ESO estimation so that each subsystem becomes approximately independent linear time invariant one without uncertainty and interaction with other subsystems. Finally, we design an ESO based output feedback for each subsystem separately to ensure that the closed-loop state is bounded, and the closed-loop output of each subsystem tracks practically a given reference signal. This is completely in comply with the spirit of active disturbance rejection control (ADRC). Some numerical simulations are presented to demonstrate the effectiveness of the proposed output feedback control scheme.

Adaptive sliding mode control with moving surface: Experimental validation for electropneumatic system

Abstract In this work, an Adaptive Sliding Mode Control (ASMC) is proposed for a class of nonlinear MIMO system with external disturbances. Although the Sliding Mode Control (SMC) is known for its precision and robustness against disturbance and uncertainties, it suffers from a chattering phenomenon and the choice of sliding surface parameters. To solve such problems, the SMC discontinuous term was replaced by a proportional derivative term and a moving sliding surface was used. The adaptive parameters were obtained by Lyapunov stability analysis to guarantee the stability of the closed loop system. In order to illustrate the efficiency of the proposed controller, experimental results on electropneumatic system were presented and compared to a classic sliding mode controller.

Solubility Optimal System for Supercritical Fluid Extraction Based on a New Nonlinear Temperature-Pressure Decoupling Model Constructed with Unequal-Interval Grey Optimal Models and Peng-Robinson Models

This paper presents a new solubility optimal system to improve the efficiency of supercritical fluid extraction (SFE). The major contribution is a nonlinear temperature-pressure decoupling model constructed with unequal-interval grey optimal models (UEIGOMs) and Peng-Robinson models (PRMs). The linear parts of temperature and pressure process can be constructed with UEIGOM, respectively. The nonlinear parts of temperature and pressure process can be described by PRMs, respectively. The whole nonlinear model cannot be input-output decoupled resulting from the singularity of decoupling matrix for PRM. This problem on input-output nondecoupling can be transformed to the problem on disturbance decoupling for a class of MIMO nonlinear systems. Therefore, the whole nonlinear coupling model can be disturbance decoupled. Furthermore, solubility optimal method is presented in the paper; it can calculate the optimal pressure according to the given temperature, namely, optimal working points, to maximize solubility for SFE process. The feasibility, effectiveness, and practicality of the proposed nonlinear temperature-pressure decoupling model constructed with UEIGOMs and PRMs are verified by SFE experiments in biphenyl. Experiments using the designed solubility optimal system are carried out to demonstrate the effectiveness in control scheme, simplicity in structure, and flexibility in implementation for the proposed solubility optimal system based on a new nonlinear temperature-pressure coupling model constructed with UEIGOMs and PRMs.

Nonlinear observer-based recurrent wavelet neuro-controller in disturbance rejection control of flexible structures

In this paper, a model-based output feedback recurrent wavelet neural network (RWNN) controller is proposed for a class of nonlinear MIMO systems with time-varying matched/mismatched uncertainties. The proposed RWNN emulator adaptively trains to follow an ideal state-feedback controller which is designed on the underlying linear model (ULM) of the plant. Simultaneously, the control system employs an adaptive neural network (NN) mechanism to estimate the mismatch between the RWNN controller and this ideal control law. As a result, the conservatism associated with the classical robust control methods where the controller is synthesized based on worst-case bounds is addressed. Moreover, in order to generalize the subjected class of the investigatable plants, the echo-state feature of adaptive RWNN is used to contribute to the performance of nonminimum phase systems. Accordingly, in the context of flexible smart structures with non-collocated sensor/actuator configuration, a delayed feedback is added in the network which brings about a better match between the model output and the measured output. As a result, even for systems with an unknown Lipschitz constant of lumped uncertainty, the controller can be trained online to compensate with an additional revision of the control law following some Lyapunov-based adaptive stabilizing rules. Additionally, the current approach is proposed as an alternative to the hot topic of nonlinear system identification-based control synthesis where the exact structure of the nonlinearity is required.

Simultaneous state and unknown input reconstruction using cascaded high-gain observers

ABSTRACTThis paper presents a systematic routine for jointly reconstruct the state variables and the unknown inputs (UIs) for a large class of nonlinear MIMO systems. After an appropriate change of state coordinates, a set of cascade high-gain observers (CHGO) are designed in such a way that each of them provides an estimation of only one component of the UI vector, except the last one which gives a final adjustment of the whole state variables. Such design achieves a boundary of the state estimation error which can be arbitrarily small by properly specifying the sole synthesis parameter. An illustrative example verifies the effectiveness of the proposed scheme.