Prescribed Performance Model-Free Adaptive Integral Sliding Mode Control for Discrete-Time Nonlinear Systems

Sliding-mode control based on prescribed performance function and its application to a SEA-Based lower limb exoskeleton

A sliding-mode control based on a prescribed performance function is proposed for discrete-time single-input single-output systems. The controller design aims to maintain the tracking error in a predefined convergence zone described by a performance function. However, due to the fixed structure of the controller, the applicability and universality of this method are limited. To address this issue, we separate the controller into two parts and analyze the principle of the prescribed performance control (PPC) method. Then we can replace the linear part of the controller with model-based control methods to adapt to the specific characteristics of the controlled system. Compared with current works, when the established system model is inaccurate, we can enhance the smoothness or response speed of the system by introducing a penalty constant to alter the system's transient characteristics while the tracking error is within the prescribed domain. Finally, numerical comparison simulations and a lower limb exoskeleton experiment illustrate the established results and the effectiveness of the proposed method.

Model-free finite-time robust control using fractional-order ultra-local model and prescribed performance sliding surface for upper-limb rehabilitation exoskeleton

To address the trajectory tracking issue of upper-limb rehabilitation exoskeleton with uncertainties and external disturbances, this paper proposes a fractional-order ultra-local model-based model-free finite-time robust controller (FO-FTRC) using predefined performance sliding surface. Different from previous model-free control strategies, a novel multi-input multi-output (MIMO) fractional-order ultra-local model which is a virtual model is proposed to approximate the complex uncertain nonlinear exoskeleton dynamics in a short sliding time window. This allows the design of controller to be independent of any exoskeleton model information and reduces the difficulty of controller design. The developed robust model-free control method incorporates a fractional-order quasi-time delay estimator (FO-QTDE), unknown disturbance estimator (UDE) as well as prescribed performance sliding mode control (PPSMC). The FO-QTDE is utilized to estimate the unknown lumped uncertainties which employs short time delayed knowledge only about the control input. However, the low-pass filter is always added for FO-QTDE when disturbances change fast, which leads to unavoidable estimation error. Then, UDE is designed to further eliminate the estimation error of FO-QTDE to enhance control performance. The PPSMC is constructed to converge sliding surface to zero in a finite time. Besides, the sliding surface is always limited in performance boundaries. After that, the overall system stability and convergence analyses are demonstrated by using the Lyapunov theorem. Finally, with the comparison to other methods of α-variable adaptive model free control (α-AMFC), time-delay estimation-based continuous nonsingular fast terminal sliding mode controller (TDE-CNFTSMC), time delay estimation (TDE)-based model-free fractional-order nonsingular fast terminal sliding mode control (MFF-TSM) and fractional-order proportion-differential (PDβ), the co-simulation results on 7-degree-of-freedom (DOF) iReHave upper-limb exoskeleton virtual prototype and experiment results on 2-DOF upper-limb exoskeleton are obtained to illustrate the effectiveness and superiority of the proposed FO-FTRC method.

Finite-time prescribed performance tracking control of seeker stabilized platform in the discrete-time domain

Current prescribed performance control (PPC) focuses on continuous-time systems, while this article proposes a novel discrete-time version of PPC for finite-time tracking of seeker stabilized platform in the discrete-time domain. Firstly, the newly developed performance functions are employed to impose finite-time prescribed performance on tracking errors. After that, a type of stabilization functions with respect to transformed errors are constructed for back-stepping controllers designing. On this basis, transformed errors are indirectly stabilized, and thus the pursued prescribed transient and steady-state behaviors are ensured for tracking errors via Lyapunov synthesis. Different from existing sliding-mode-control based discrete-time PPC, the addressed approach eliminates the sliding-mode structure and hence avoids high frequency chattering caused by such framework. Finally, compared simulations validate the superiority over existing methods.

Fault Estimation and Control for Unknown Discrete-Time Systems Based on Data-Driven Parameterization Approach

This study investigates the problem of fault estimation and control for unknown discrete-time systems. Such a problem was first formulated as an H_∞/H_∞ multiobjective optimization problem. Then, a data-driven parameterization controller design method was proposed to optimize both fault estimation and robust control performances. In terms of the single-objection H_∞ control problem, necessary and sufficient conditions for designing the H_∞ suboptimal controller were presented, and the H_∞ performance index optimized by the developed data-driven method was shown to be consistent with that of the model-based method. In addition, by introducing additional slack variables into the controller design conditions, the conservatism of solving the multiobjective optimization problem was reduced. Furthermore, contrary to the existing data-driven controller design methods, the initial stable controller was not required, and the controller gain was directly parameterized by the collected state and input data in this work. Finally, the effectiveness and advantages of the proposed method are shown in the simulation results.

Model-Free Adaptive Control of Hydrometallurgy Cascade Gold Leaching Process with Input Constraints

Hydrometallurgy technology can directly deal with low grade and complex materials, improve the comprehensive utilization rate of resources, and effectively adapt to the demand of low carbon and cleaner production. A series of cascade continuous stirred tank reactors are usually applied in the gold leaching industrial process. The equations of leaching process mechanism model are mainly composed of gold conservation, cyanide ion conservation, and kinetic reaction rate equations. The derivation of the theoretical model involves many unknown parameters and some ideal assumptions, which leads to difficulty and imprecision in establishing the accurate mechanism model of the leaching process. Imprecise mechanism models limit the application of model-based control algorithms in the leaching process. Due to the constraints and limitations of the input variables in the cascade leaching process, a novel model-free adaptive control algorithm based on compact form dynamic linearization with integration (ICFDL-MFAC) control factor is first constructed. The constraints between input variables is realized by setting the initial value of the input to the pseudo-gradient and the weight of the integral coefficient. The proposed pure data-driven ICFDL-MFAC algorithm has anti-integral saturation ability and can achieve faster control rate and higher control precision. This control strategy can effectively improve the utilization efficiency of sodium cyanide and reduce environmental pollution. The consistent stability of the proposed control algorithm is also analyzed and proved. Compared with the existing model-free control algorithms, the merit and practicability of the control algorithm are verified by the practical leaching industrial process test. The proposed model-free control strategy has advantages of strong adaptive ability, robustness, and practicability. The MFAC algorithm can also be easily applied to control the multi-input multi-output of other industrial processes.

Gradient Descent-Barzilai Borwein-Based Neural Network Tracking Control for Nonlinear Systems With Unknown Dynamics

In this article, a combined gradient descent-Barzilai Borwein (GD-BB) algorithm and radial basis function neural network (RBFNN) output tracking control strategy was proposed for a family of nonlinear systems with unknown drift function and control input gain function. In such a method, a neural network (NN) is used to approximate the controller directly. The main merits of the proposed strategy are given as follows: first, not only the NN parameters, such as weights, centers, and widths but also the learning rates of NN parameter updating laws are updated online via the proposed learning algorithm based on Barzilai-Borwein technique; and second, the controller design process can be further simplified, the controller parameters that should be tuned can be greatly reduced. Theoretical analysis about the stability of the closed-loop system is manifested. In addition, simulations were conducted on a numerical discrete time system and an inverted pendulum system to validate the presented control strategy.

Predefined performance-based model-free adaptive fractional-order fast terminal sliding-mode control of MIMO nonlinear systems

The purpose of this article is to tackle with the problem of data-driven robust control of multi-input multi-output discrete-time nonlinear plants under tracking error constraints and output perturbations. Thereby, based upon the concept of dynamic linearization, a novel predefined performance based model-free adaptive fractional-order fast terminal sliding-mode controller is proposed so that the tracking errors can converge and remain within a preassigned neighborhood. The presented approach does solely rely on the real-time input/output data of the process, and the transient response together with the steady-state manner of the errors can be arbitrarily predefined. In the meantime, the closed-loop behavior is investigated by mathematical analysis, and the efficiency of the method is validated through various simulation examples.

Data-driven adaptive integral terminal sliding mode control for uncertain SMA actuators with input saturation and prescribed performance

This paper focuses on the data-driven adaptive control problem of the shape memory alloy (SMA) actuators subject to uncertainties, input saturation and prescribed performance. Firstly, the uncertainties estimation method, anti-windup technology, and prescribed performance function are introduced to deal with uncertain nonlinearity, input constraint, and prespecified performance, respectively. Meanwhile, a general approach about designing asymmetrical convergence bound is presented to increase the flexibility of creating convergence area. Secondly, taking uncertainties, input saturation, and asymmetrical convergence bound into consideration, we design an integral terminal sliding mode controller to guarantee the prescribed tracking accuracy without using the knowledge of the SMA actuators model. Further, the stability of the controller and the boundedness of the convergence error are proved by rigorous theoretical analysis. Finally, the success and superiority of our controller are verified by the SMA actuator experiments.

Design of active fault-tolerant control system for Air-fuel ratio control of internal combustion engines using fuzzy logic controller

BACKGROUND

Fault-Tolerant Control Systems (FTCS) are used in critical and safety applications to improve performance and stability despite failure modes. As a result, costly production losses related to unusual and unplanned shutdowns can be prevented by incorporating these systems in the critical process plant machines. The Internal Combustion (IC) engines are highly used process plant machines and faults in their sensors will cause their shutdown instigating the need to install FTCS in them.

INTRODUCTION

In this paper, an Active Fault-Tolerant Control System (AFTCS) based on a Fuzzy Logic Controller (FLC) is suggested to improve the reliability of the Air-Fuel Ratio (AFR) control system of an IC engine.

METHODOLOGY

For analytical redundancy, a nonlinear Fuzzy Logic (FL) based observer is implemented in the proposed system for the Fault Detection and Isolation (FDI) unit for nonlinear sensors of the AFR system. Lyapunov stability analysis was used for designing a stable system in both faulty and normal conditions. To evaluate its performance, this system was developed in the MATLAB/Simulink platform.

RESULTS

The simulation results show that the developed system is robust under sensor fault conditions, retaining stability with a minimum decrease of AFR. This study's comparison with the existing literature demonstrates that the proposed system is effective for maintaining the AFR in IC engines during sensor faulty conditions thus reducing shutdown of engine and production loss for increased profits.

Prescribed performance model-free adaptive sliding mode control of a shape memory alloy actuated system

This paper concentrates on a simple and robust control method for the discrete time nonlinear systems to fulfill the requirement of predefined accuracy. A sliding mode control method is designed by introducing equivalent dynamic linearization technique according to the input/output (I/O) information merely. A square-root type error transformation method is presented for the tracking error to be restricted within a preassigned zone. The performance of presented control method is demonstrated through experiments on a nonlinear system. Experiment results show that the presented control method has a superior tracking accuracy compared with PID controller and model-free adaptive control (MFAC).

Adaptive Integral Sliding Mode Based Course Keeping Control of Unmanned Surface Vehicle

This paper investigates the course keeping control problem for an unmanned surface vehicle (USV) in the presence of unknown disturbances and system uncertainties. The simulation study combines two different types of sliding mode surface based control approaches due to its precise tracking and robustness against disturbances and uncertainty. Firstly, an adaptive linear sliding mode surface algorithm is applied, to keep the yaw error within the desired boundaries and then an adaptive integral non-linear sliding mode surface is explored to keep an account of the sliding mode condition. Additionally, a method to reconfigure the input parameters in order to keep settling time, yaw rate restriction and desired precision within boundary conditions is presented. The main strengths of proposed approach is simplicity, robustness with respect to external disturbances and high adaptability to static and dynamics reference courses without the need of parameter reconfiguration.