Control Design For Nonlinear Systems Research Articles

Robust adaptive control design of nonlinear systems with input delay

AbstractIn this paper a robust adaptive controller for a class of uncertain nonlinear systems is developed with additive disturbance and unknown time‐varying input delay. The control law is composed of a Desired Compensation Adaptation Law (DCAL) based feedforward term for the adaptation of uncertain plant parameters and two robust feedback terms based on the integral of the past control to compensate the input delay. The sufficient conditions on controller gains and limit on delay bound are derived through stability analysis by choosing suitable Lyapunov‐Krasovskii functionals which gives a globally uniformly ultimately bounded (GUUB) tracking. The performance of the controller is evaluated by performing simulation on a two link robot manipulator system for different values of the input delay.

Robust fault-tolerant tracking control for a class of T-S fuzzy systems subject to actuator failure and external disturbance

Based on the Takagi-Sugeno (T-S) fuzzy model approach, this study discusses the robust fault-tolerant tracking controller design for non-linear systems affected by external disturbances, uncertainties, and actuator failures. In contrast to existing results, this study assumes the actuator fault model includes linear and nonlinear terms, and a state feedback controller is designed to improve the tracking and stability of the system when actuators fail. Using a non-quadratic Lyapunov function, new sufficient conditions for L_2-gain tracking performance analysis are derived to determine simultaneously the minimal level of the L_2-gain and controller gains. The robustness of the proposed approach is also investigated. An illustration of the theoretical developments is provided by a Duffing forced oscillation system.

Limitations of FxLMS in Feedforward Active Vibration Control of a Nonlinear Two-Degree-of-Freedom System

Active control systems are often used to surmount the challenges associated with passive noise and vibration control measures to control low frequency disturbances, since they achieve control without the application of large or heavy control treatments. Historically, linear active control strategies have been used in feedforward control systems to drive the control source to minimise the signal measured at the error sensor. Amongst the various control algorithms available, the Filtered-reference Least Mean Squares (FxLMS) algorithm has become extremely popular in the last few decades due to its relatively good performance and high level of robustness, as well as simplicity in both design and application. However, when the system under control contains nonlinearities, either in the primary or secondary paths, the performance of the FxLMS algorithm can degrade dramatically. This paper explores the performance limitations of the FxLMS algorithm when applied to the control of a two degree of freedom mass-spring-damper system with linear and cubic nonlinear stiffness terms. The aim of this study is to improve understanding of and inspire better design of nonlinear control systems. The statistical uncertainty present in the linear plant model and control filter is discussed, as well as the effect of this on control performance and control effort. The effect of nonlinearity on the maximum convergence parameter of the algorithm is also discussed.

Data-based control design for nonlinear systems with recurrent neural network-based controllers

This paper addresses the design of controllers for systems modelled as recurrent neural networks (RNNs). A novel data-based procedure for the design of RNN-based regulators is proposed, guaranteeing closed-loop stability properties and desired performances, conferred by virtual reference feedback tuning. The approach is tested on a realistic nonlinear system.

Adaptive delay dependent sliding mode fault-tolerant controller design for nonlinear systems with unknown time-varying input and state delays

This paper presents a novel adaptive delay-dependent fault-tolerant sliding mode control (SMC) strategy for the class of nonlinear Lipschitz systems with time-varying unknown delays in system states and inputs. A modified integral sliding surface (ISS) based on which the SMC approach is developed using a linear matrix inequality. Lyapunov-Krasovskii stability theory is employed to guarantee asymptotic stability of the closed-loop system such that system states starting from any arbitrary initial conditions with time-varying delays reach the predefined sliding surface in a finite time. It is also proved that states stay on the surface for all subsequent time, and the effects of the actuator’s faults are simultaneously attenuated. Adaptive tuning laws are used to adjust controller parameters and estimate actuators’ faults. The controllers’ structures are more straightforward than the most existing recent fault-tolerant control methods. Simulation results of practical nonlinear inverted pendulum system verified the outstanding merits and capabilities of the proposed scheme in the presence of actuators’ faults and multiple delays in the system states and inputs.

A new adaptive second‐order sliding mode controller design for nonlinear systems with multiple uncertainties

SummaryThis study is dedicated to solving the problem of a new adaptive second‐order sliding mode (SOSM) controller design for a type of nonlinear systems with multiple uncertainties by using adding a power integrator (API) and the parameter separation techniques. Supported by the finite‐time Lyapunov theory, the finite‐time stability of the closed‐loop system under the proposed adaptive SOSM controller has been firmly guaranteed. The significant advantages here lie in that the prior knowledge about the bounds of uncertainties is not required in the designed adaptive SOSM control approach, and the switching gain can be tuned dynamically. Finally, a numerical example is presented to indicate the notable feature and effectiveness of the designed adaptive SOSM approach.

Stochastic optimisation algorithm for optimisation of controller parameters for control of dissolved oxygen in wastewater treatment plant

Wastewater treatment plants (WWTPs) are very important facilities for mankind. They enable the removal and neutralisation of man-made pollutants. Therefore, it is important for wastewater treatment plants to operate as efficiently as possible so that the level of pollutants in the treated wastewater meets specific requirements. This paper concerns the design of a hierarchical nonlinear adaptive control system for dissolved oxygen (DO) concentration in wastewater for a biological Sequential Batch Reactor (SBR). The parameters of the control system used are optimised to ensure the best possible control quality and low energy consumption at the same time. Based on data collected from a case study WWTP, an Activated Sludge Model 2d (ASM2d) of the biological processes and a model of the aeration system are applied. The Coyote Optimization Algorithm (COA) is used to optimize the adaptive controller parameters. A Proportional-Integral-Derivative (PID) control system is also developed to compare the control results. The results obtained from simulation studies for both control systems are presented. As a result of optimised parameters, higher wastewater treatment efficiency and reduced electricity consumption are achieved.

Adaptive Finite-Time Command Filtered Controller Design for Nonlinear Systems With Output Constraints and Input Nonlinearities.

This work addresses a finite-time tracking control issue for a class of nonlinear systems with asymmetric time-varying output constraints and input nonlinearities. To guarantee the finite-time convergence of tracking errors, a novel finite-time command filtered backstepping approach is presented by using the command filtered backstepping technique, finite-time theory, and barrier Lyapunov functions. The newly proposed method can not only reduce the complexity of computation of the conventional backstepping control and compensate filtered errors caused by dynamic surface control but also can ensure that the output variables are restricted in compact bounding sets. Moreover, the proposed controller is applied to robot manipulator systems, which guarantees the practical boundedness of all the signals in the closed-loop system. Finally, the effectiveness and practicability of the developed control strategy are validated by a simulation example.

A Sum of Squares-Based Approach to Robust Nonlinear Mixed H2/H∞ Output-Feedback Control for a Class of Uncertain Polynomial Systems

This paper considers the robust nonlinear mixed H2/H∞ output-feedback control problem for a class of uncertain polynomial systems. Generally, the solvable conditions of such nonlinear output-feedback control problems are nonconvex, whose computations are challenging. By using the semidefinite programming relaxation technique based on sum of squares (SOS) decomposition, the solvable conditions of above control problem are formulated in terms of state-dependent linear matrix equality (LMI), which can be effectively solved. This conversion effectively overcomes the computational difficulties caused by the non-convexity of output-feedback H∞ control design for nonlinear systems. Furthermore, the state-observer and the controller can be designed simultaneously through a single-step SOS condition and constructed in a simple analytical form, thus reducing the computational complexity in a certain degree. In the simulation, the nonlinear mass-spring-damper system is considered to illustrate the effectiveness and feasibility of the proposed approach. The results show that the proposed method not only guarantees the stability of the system, but also has good transient performance and robust performance.

Finite-time adaptive neural network command filtered controller design for nonlinear system with time-varying full-state constraints and input quantization

In this paper, an adaptive finite-time command filtered control scheme is investigated for a class of nonlinear systems with asymmetric time-varying full state constraints and input quantization. Firstly, by fusing the backstepping control method and command filter technique, a novel adaptive neural networks (NNs) command filtered control approach is proposed. Moreover, a modified error compensation mechanism is constructed to compensate for the filtering error. Secondly, a smooth nonlinear transformation is constructed to eliminate the influence brought by the actuator subject to input quantization. Based on the constructed asymmetric time-varying barrier Lyapunov function (TVBLF), the strict constraints are guaranteed not to be violated and the stability of the closed-loop system is achieved in finite-time. Finally, simulations are carried out to illustrate the effectiveness of the theoretical results.

A switching-free multiple-model approach for adaptive FTC of non-Lipschitz nonlinear uncertain systems under persistent actuator failures

A novel actuator failure compensation scheme is proposed for affine nonlinear uncertain systems (not necessarily Lipschitz) subject to persistent/intermittent actuator faults/failures unknown in time, magnitude and pattern. The proposed control methodology satisfies the nonlinear separation principle through a modular backstepping control. The controller is then augmented with multiple estimation models to estimate failure induced parametric uncertainties and unknown system parameters. The output transient performance at start up and post-failure instances, is improved on account of a two layer adaptation which enhances the convergence speed and accuracy of parameter estimates. The proposed fault tolerant control (FTC) method yields a faithful accommodation of uncertain finite as well as infinite/intermittent/persistent actuator failures while ensuring satisfactory output transient and steady state performances. Further, compared to existing multiple model based adaptive fault tolerant control design for nonlinear systems, the proposed methodology circumvents the issues of stability due to switching between different models and utilizes a minimum number of estimation models for parameter estimation without compromising on the output performance. Consequently, the computational burden is also reduced. Compared to multiple model adaptive control based FTC strategies proposed earlier which assume finite actuator failures and Lipschitz nonlinear system, the proposed method is applicable to both Lipschitz and non-Lipschitz nonlinear systems affected by intermittent actuator failures. Using the concepts from stability analysis in random nonlinear impulsive systems, the L∞ and L2 bounds on tracking error for all future time are derived in the case of intermittent/persistent actuator failures obtained using the proposed fault-tolerant controller. The improvement of output transient performance in the proposed control scheme in comparison with controller with single identifier, is theoretically proved and quantified.

Fault‐tolerant controller design for nonlinear systems with multiple input and state delays based on sliding mode algorithm

AbstractIn this article, a novel sliding mode control (SMC) strategy for nonlinear Lipschitz systems with multiple and dissimilar time delays in the states and inputs is proposed. Using linear matrix inequality, a modified integral sliding surface scientifically based on which the innovative SMC approach is developed. Lyapunov–Krasovskii's theory is employed to guarantee asymptotic stability of the closed‐loop system, such that states starting from any arbitrary initial conditions reach the sliding surface in a finite time and stay on it for all subsequent time. It is also proved that the practical effects of the actuator's faults are simultaneously attenuated. An online adaptive tuning law is used to estimate and isolate actuators' possible faults reliably. From the implementation point of view, the controller structure is more straightforward than the most existing recent fault‐tolerant control methods. Simulation results performed on practical nonlinear systems (quadruple tank and industrial continuous stirred tank reactor) verified the outstanding merits of the proposed approach. The operational capabilities of the proposed scheme in the presence of actuators' faults and multiple delays in the states and inputs were also demonstrated.

Improved Design of Nonlinear Control Systems with Time Delay

It is well known that time delay in nonlinear control systems may lead to the deterioration or even destabilization of the closed-loop systems. Therefore, specific analysis techniques and design methods are needed to be developed for nonlinear control systems in the presence of time delay. This chapter aims to give a broad overview of the stability and control of nonlinear time-delay systems. Firstly, we present some motivations and a comprehensive survey for the study of time-delay systems. Then, a brief overview of some control approaches is provided, specifically, the Lyapunov-Krasoviskii functional method for high-order polynomial uncertainties nonlinear time-delay systems, and nonlinear time-delay systems with nonlinear input, the Lyapunov-Razumikhin method for triangular structure nonlinear time-delay systems, dynamic gain control for full state time-delay systems. Finally, an application in chemical reactor systems is provided and some related open problems are discussed.

On Controller Design for Nonlinear Systems With Pure State Constraints

This brief is concerned with a new problem of designing a robust adaptive backstepping controller for nonlinear systems where state constraints are an explicit function of time and state variables, i.e., pure state constraints. Furthermore, a disturbance observer is designed to cope with the disturbances in the systems. Finally, a numerical example is demonstrated to show the efficacy of the proposed theoretical results.

Observer-Based Control Design for Nonlinear Systems With Unknown Delays

In this brief, we study the problem of designing observer-based controller for nonlinear system subject to unknown time-varying state delay. The unknown delay is assumed to be upper bounded, but nevertheless the bound is not required to be known. In order to tackle this interesting problem, we utilize a Halanay-inequality-based criterion which can guarantee exponential stability of the closed-loop system as well as the estimation error system. This exponential stability criterion allows us to design observer-based controller for the nonlinear time-delay system without invoking differentiability assumption on the unknown delay. A robotic system is considered to illustrate the efficiency of the new results.

DESIGN OF DYNAMIC NONLINEAR INTELLIGENT CONTROL SYSTEM FOR SIGNAL PROCESSING

Based on back propagation neural network (BPNN), we design a dynamic nonlinear intelligent control system for signal processing and analysis in this work. Performances of the traditional PID and BPNN control systems is compared in a case of heat power engineering system design. In the design, the training times, regulation time of the BPNN control system are evaluated when [Formula: see text] and [Formula: see text], respectively. Furthermore, the regulation time, oscillation time and amplitude of the traditional PID and BPNN control systems are compared in the dead zone. Results of the comparison show that the BPNN based dynamic nonlinear intelligent control system demonstrates superior performances over the traditional PID control system. The research results prove the advantage of BPNN in the design of nonlinear control systems and provide a scientific and effective reference for the follow-up research works.

Switched Control Design for Nonlinear Systems Using State Feedback

Switched Control Design for Nonlinear Systems Using State Feedback

Sampled-Data Stabilization With Control Lyapunov Functions via Quadratically Constrained Quadratic Programs

Controller design for nonlinear systems with Control Lyapunov Function (CLF) based quadratic programs has recently been successfully applied to a diverse set of difficult control tasks. These existing formulations do not address the gap between design with continuous time models and the discrete time sampled implementation of the resulting controllers, often leading to poor performance on hardware platforms. We propose an approach to close this gap by synthesizing sampled-data counterparts to these CLF-based controllers, specified as quadratically constrained quadratic programs (QCQPs). Assuming feedback linearizability and stable zero-dynamics of a system's continuous time model, we derive practical stability guarantees for the resulting sampled-data system. We demonstrate improved performance of the proposed approach over continuous time counterparts in simulation.

Iterative Learning Control Design for Nonlinear Systems with Reference Trajectory Switching

This paper continues the development of iterative learning control for systems performing the same finite duration task repeatedly. Each execution is known as a trial, and the finite duration of each trial is known as the trial length. In many designs the reference trajectory is not changed during the generation of the trials, but there are applications where changing, or switching, this trajectory is required. Design in this case has been addressed based on a linear model for the dynamics, and there has been some results on design for examples where a nonlinear model of the dynamics has to be used. The development of this latter case based on the use of the recently developed vector Lyapunov function-based stability theory for nonlinear repetitive processes combined with feedback linearization is the subject of this paper. Moreover, the case when the reference trajectory is required to switch after a number of trials have been completed is considered and a switching rule is developed to avoid to avoid the increase in the tracking error after switching occurs.

Stabilizing Controller Design for Nonlinear Systems Based on the H∞ Norm and Prefilter

This study analyzes the design of stabilization controllers for nonlinear systems. The proposed method is based on the synthesis control method of the H∞ norm and prefilter, which is a low-pass filter. The low-pass filter is coupled to structure an open-loop transfer function such that sensitivity and complementary sensitivity functions possess desirable frequency characteristics. The H∞ controller, which was designed to validate the proposed controller method, was applied to a representative nonlinear system of an inverted pendulum system, and results were compared with the with that of a PID controller application. Simulation results show that the designed controller well adhered to control objectives while reducing the influence of modeling error and noise.