Sliding mode control of uncertain systems with distributed time-delay: parameter-dependent Lyapunov functional approach

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities (LMIs), which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.     

Sliding mode control of uncertain systems with distributed time-delay： parameter-dependent Lyapunov functional approach

The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities （LMIs）, which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme.     

Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer, for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements. A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains, which will give enough flexibility in the choice of initial estimates. Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.      

基于粒子群优化的分数阶PID滑模控制参数整定

为了提高系统的控制性能,解决单一控制方法不足,将分数阶PID算法与滑模变结构算法相结合,同时为了规避分数阶PID的滑模变结构算法手动调节参数的复杂性以及不确定性,采用粒子群算法对其参数进行优化,完善分数阶PID的滑模变结构控制器,提高其控制精度.并将新型算法应用于单相全桥逆变器,通过Matlab仿真并与分数阶PID滑模变结构控制函数(PID-SMC)及滑模变结构控制(SMC)方法相比较,研究结果表明,粒子群算法整定参数收敛速度快,较短时间内可以找出最优解,整定后的算法静态误差小,上升速度快,抑制系统抖振能力强,具有较强的鲁棒性.     

高阶滑模控制在非完整移动机器人鲁棒输出跟踪中的应用

给出了移动机器人鲁棒输出跟踪的高阶滑模控制器, 它不仅可以削弱滑模控制系统的抖振问题, 还对系统存在的不确定性具有良好的鲁棒性. 数值仿真表明了该控制器的有效性.     

Using genetic algorithms to optimize the design parameters of generalized predictive controllers

Generalized predictive control algorithms are a powerful control design method widely applied to industrial processes. However, there is no easy way to tune the design parameters, mainly prediction and control horizons, in order to achieve optimal performance. In this work, a genetic algorithm is proposed whose aim is to find on line the optimal values for the tuning parameters.     

Adaptive backstepping sliding mode control with tuning functions for nonlinear uncertain systems

An adaptive backstepping tuning functions sliding mode controller is proposed for a class of strict-feedback nonlinear uncertain systems. In this control design, adaptive backstepping is used to deal with unknown or uncertain parameters and the matching condition restricting the Lyapunov based design. The main drawback of the Lyapunov based adaptive backstepping which is the overparametrisation is eliminated by the tuning functions. The adaptive backstepping tuning functions design is combined with the sliding mode control in order to overcome quickly varying parametric and unstructured uncertainties, and to obtain chattering free control. The proposed controller not only provides robustness property against uncertainty but also copes with the overparametrisation problem. Experimental results of the proposed controller are compared with those of the standard sliding mode controller. The proposed controller exhibits satisfactory transient performance, good estimates of the uncertain parameters, and less chattering.     

Robustness and performance parameterization of smooth second order sliding mode control

Novel robustness and performance parameters are established for Smooth Super Twisting Algorithm (SSTA). The stability of SSTA is well established for arbitrary gains using homogeneity approach. The design and tuning of the controller parameters is a major issue and no analytic design method is available so far. A novel Lyapunov function is proposed and by the virtue of stability analysis, the stability bounds for a certain class of uncertainties are determined. In addition, the issue of finite time convergence is also explored, resulting in determination of the settling time as a function of the controller parameters. The proposed settling time formulation suggests a methodical approach to SSTA design in contrast to the available rules of thumb. Unlike the literature available for Higher Order Sliding Mode (HOSM) controllers, the proposed design framework is validated against a challenging problem of the Underground Coal Gasification (UCG) process control. Like the other process control problems the chosen problem is nonlinear and contains significant uncertainties.     

High-Order Sliding Modes for a Robot Driven by Pneumatic Artificial Rubber Muscles

It is known that classical sliding mode control generates chatter which is undesirable. One way to reduce this chatter is the use of high-order sliding mode (HOSM) control. The HOSM control techniques are applied to the first 2 d.o.f. of a robot actuated by pneumatic artificial rubber muscles (PARMs). The PARMs are arranged in opposite pairs (antagonistic configuration). The objective is to show that without the use of the equivalent control, it is still possible to control the robot by the use of HOSM and at the same time reduce the chatter. Experimental results are presented and comparison between two second-order sliding controls established.     

液压驱动伺服机器人的模糊滑模控制研究

针对液压驱动四足机器人伺服系统非线性和不确定性严重的问题,提出了一种快速响应、鲁棒性好、控制精度高的模糊滑模控制器,并进行了仿真研究.首先,建立了液压驱动伺服机器人的液压动力机构非线性数学模型,利用Lyapunov方法设计了滑模控制器;其次,构造了一个模糊边界层宽度调节器,削弱滑模控制的抖振;最后,分析了参考力、液压参数、供油压力及负载刚度变化对系统输出的影响.仿真结果表明,该控制器对液压伺服力系统非线性和参数变化具有较好的控制效果.该方法用于四足液压驱动伺服机器人的控制是可行的、有效的.     

Two relay controller for real time trajectory generation and its application to inverted orbital stabilization of inertia wheel pendulum via quasi‐continuous HOSM

A quasi‐continuous high‐order sliding mode (QC‐HOSM) control is developed to solve the tracking control problem for an inertia wheel pendulum. A first step towards the solution of the tracking control problem in underactuated systems is to find the set of reference trajectories. A reference model based on the two relay controller idea is then developed for generating a set of desired periodic trajectories for the pendulum centered at its upright position. The two relay controller produces oscillations at the scalar output of the reference underactuated system where the desired amplitude and frequency are reached by choosing its gains. The HOSM will be capable of making the pendulum move, tracking the prescribed reference signals determined by the trajectory generator. Performance issues of the controller constructed are illustrated in an experimental study. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Sliding mode control approaches to the robust regulation of linear multivariable fractional‐order dynamics

Sliding mode control approaches are developed to stabilize a class of linear uncertain fractional‐order dynamics. After making a suitable transformation that simplifies the sliding manifold design, two sliding mode control schemes are presented. The first one is based on the conventional discontinuous first‐order sliding mode control technique. The second scheme is based on the chattering‐free second‐order sliding mode approach that leads to the same robust performance but using a continuous control action. Simple controller tuning formulas are constructively developed along the paper by Lyapunov analysis. The simulation results confirm the expected performance. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive integral higher order sliding mode controller for uncertain systems

This paper proposes an adaptive integral higher order sliding mode (HOSM) controller for uncertain systems. Instead of a regular control input, the derivative of the control input is used in the proposed control law. The discontinuous sign function in the controller is made to act on the time derivative of the control input. The actual control signal obtained by integrating the derivative control signal is smooth and chattering free. The adaptive tuning law used in the proposed controller eliminates the need of prior knowledge about the upper bound of the system uncertainties. Stability and robustness of the proposed controller are proved by using the classical Lyapunov criterion. Simulation results demonstrate the advantages of the proposed control scheme.     

Observability Analysis and Improved Zero‐Speed Position Observer Design of Synchronous Motor with Experimental Results

This paper deals with the permanent magnet synchronous motor (PMSM) observability analysis for sensorless control design. The problem of loss of observability at low frequency range is always recognized in experimental settings. Nevertheless, there are no sufficient theoretical observability analyses for the PMSM. In the literature, only the sufficient observability condition has been presented. Therefore, the current work is aimed especially towords the necessary observability condition analysis. Furthermore, improved zero‐speed observation is presented here for a surface PMSM (SPMSM) to overcome position observability problems at zero‐speed which is an unobservable state point. The proposed observer based on higher order sliding mode (HOSM) is designed in order to ensure robustness against disturbances and to avoid the chattering phenomenon which is inherent in standard first order sliding modes. The stability and finite time convergence of the developed observer are studied and discussed. Experimental results are carried out to illustrate the effectiveness and robustness of the proposed observer.     

面向小型无人机导航的滑模控制算法研究

设计一种简单、高效、稳健的导航算法对无人机来说非常重要。分析了无人机的运动学和动力学特性,提出了一种基于滑模控制理论的非线性导航算法。针对滑模控制中出现的抖振问题,重新进行了控制律设计,并对制导参数进行了优化。实际测试结果表明,所提出的导航控制算法具有良好的性能指标,可跟踪任意航路点,可实现无人机自主飞行。     

Optimal Robust Control for Unstable Delay System

Proportional-Integral-Derivative control system has been widely used in industrial applications. For uncertain and unstable systems, tuning controller parameters to satisfy the process requirements is very challenging. In general, the whole system’s performance strongly depends on the controller’s efficiency and hence the tuning process plays a key role in the system’s response. This paper presents a robust optimal Proportional-Integral-Derivative controller design methodology for the control of unstable delay system with parametric uncertainty using a combination of Kharitonov theorem and genetic algorithm optimization based approaches. In this study, the Generalized Kharitonov Theorem (GKT) for quasi-polynomials is employed for the purpose of designing a robust controller that can simultaneously stabilize a given unstable second-order interval plant family with time delay. Using a constructive procedure based on the Hermite-Biehler theorem, we obtain all the Proportional-Integral-Derivative gains that stabilize the uncertain and unstable second-order delay system. Genetic Algorithms (GAs) are utilized to optimize the three parameters of the PID controllers and the three parameters of the system which provide the best control that makes the system robust stable under uncertainties. Specifically, the method uses genetic algorithms to determine the optimum parameters by minimizing the integral of time-weighted absolute error ITAE, the Integral-Square-Error ISE, the integral of absolute error IAE and the integral of time-weighted Square-Error ITSE. The validity and relatively effortless application of presented theoretical concepts are demonstrated through a computation and simulation example.     

Longitudinal control of an intelligent vehicle using particle swarm optimization based sliding mode control

This paper focuses on the design of longitudinal controller for an intelligent vehicle which was built at Asian Institute of Technology based on sliding mode control. The proposed controller uses particle swarm optimization (PSO) for optimal tuning of sliding surface and controller gain in the sliding mode controller (SMC). The longitudinal control is conducted via controlling of throttle value angle using PSO-based SMC on the simplified first-order linear model of the intelligent vehicle and controlling of brake force using fuzzy logic. In order to achieve the desired headway time, integration of throttle valve angle control and brake force control is required. To obtain the optimal parameters of SMC, two equations velocity updating and position updating are applied. Firstly, the performance of proposed controller is evaluated by using MATLAB simulation to compare with conventional PD controller. Finally, the experimental results show that the proposed PSO-based SMC can perform efficiently in longitudinal control of the intelligent vehicle.     

不确定离散切换系统的滑模控制

研究一类不确定离散切换系统的鲁棒滑模控制问题.针对传统变结构控制应用于离散系统时易失去其鲁棒性的问题,提出一种采用带调整参数递归式滑模函数的离散滑模控制策略,改进了离散时间滑模控制系统的趋近律方法,并针对不确定因素的影响设计了无须知道扰动上界的估计器.应用Lyapunov函数给出了离散切换系统的滑动模态可达条件,并设计了离散切换规则.仿真结果表明了所提出设计方法的有效性.     

Cascade fuzzy variable structure control of induction motor based on the approach of fuzzy modelling of Ben-Ghalia

In this article, a control design concept using fuzzy sets for an induction motor is presented. The aim of the proposed modelling approach is to provide a fuzzy set-based representation of the cascade sliding mode control of an induction motor fed by PWM voltage source inverter, which operates in a fixed reference frame. For this purpose, a new decoupled and reduced model is first proposed. Then, a set of simple surfaces and associated control laws are synthesised. A piecewise smooth control function with a threshold is adopted. However, the magnitude of this function depends closely on the upper bound of uncertainties, which include parameter variations and external disturbances. This bound is difficult to obtain prior to motor operation. To solve this problem, a fuzzy modelling approach is presented to improve the design and tuning of a fuzzy logic controller using variable structure control theory. The robust fuzzy control design is made feasible without resorting to model simplification or imposing restrictive conditions on the system uncertainty. The fuzzy controller is designed in order to improve the control performances and to reduce the control energy and the chattering phenomenon. Simulation results reveal some very interesting features and show that the proposed fuzzy sliding mode controller could be considered as an alternative to the conventional sliding mode control of induction motors.     

Adjustment of high‐order sliding‐mode controllers

Long‐lasting problems of high‐order sliding‐mode (HOSM) design are solved. Only local uncertainty suppression was previously obtained in the case when the dynamic system uncertainties are unbounded. This restriction is removed in this paper. A universal method is proposed for the proper controller parameter adjustment based on the homogeneity approach. The method allows making the finite‐time convergence arbitrarily fast or slow. In addition, a HOSM regularization procedure is proposed diminishing chattering. Computer simulation confirms the theoretical results. Copyright © 2008 John Wiley & Sons, Ltd.