NETWORK‐INDUCED DELAY‐DEPENDENT H∞ CONTROLLER DESIGN FOR A CLASS OF NETWORKED CONTROL SYSTEMS

This paper is concerned with the problem of robust H_∞ controller design for a class of uncertain networked control systems (NCSs). The network‐induced delay is of an interval‐like time‐varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time‐varying. Based on Lyapunov‐Krasovskii functional approach, a robust H_∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay‐dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H_∞ performance level of the closed‐loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.     

A hybrid controller design for bi‐axial inverted pendulum system

This study presents the use of Tustin's friction model and a disturbance observer (DOB) to improve the steady‐state error (SSE) of a bi‐axial inverted pendulum–cart system (IPCS). Furthermore, a hybrid controller contains a feedback linearization control for pendulum angle in the region of 3–12° to enlarge the angle of operation and an H_∞ control using loop shaping design procedure (LSDP) for cart position and pendulum angle in the region of 0–3° to stabilize the IPCS, respectively. Experimental results reveal that the pendulum maximum angle of operation is improved from 7 to 12°; the SSE of the angle of the pendulum is reduced from 0.85 to 0.1°, and the SSE of the position of the cart is reduced from 10 to 1.4 mm. Experimental results are illustrated and films are provided at the web site http://hinfinity.myweb.hinet.net to show the effectiveness and robustness of the hybrid controller with Tustin's friction model and DOB compensation. Copyright © 2008 John Wiley & Sons, Ltd.     

An Improved Anti‐Windup Bumpless Transfer Structures Design for Controllers Switching

In this paper, an anti‐windup bumpless transfer (AWBT) control structure combined with linear interpolation method is proposed for smooth switching control. By choosing an appropriate scheduling signal, different controllers can be switched smoothly under a unified framework. Meanwhile, some robust specifications including H₂/H_∞ performance, pole placement constraint, and passivity of the closed‐loop system can be preserved through controller switching. Furthermore, for the linear system subject to input saturation, the stability and L₂ gain of the closed‐loop system can be guaranteed. Finally, a cart‐spring pendulum system is simulated to demonstrate the effectiveness of the proposed scheme.     

Robust non‐fragile H ∞ ∕ L2 − L ∞ control of uncertain linear system with time‐delay and application to vehicle active suspension

This paper presents an approach to design robust non‐fragile H _∞ ∕ L₂ ? L _∞ static output feedback controller, considering actuator time‐delay and the controller gain variations, and it is applied to design vehicle active suspension. According to suspension design requirements, the H _∞ and L₂ ? L _∞ norms are used, respectively, to reflect ride comfort and time‐domain hard constraints. By employing a delay‐dependent Lyapunov function, existence conditions of delay‐dependent robust non‐fragile static output feedback H _∞ controller and L₂ ? L _∞ controller are derived, respectively, in terms of the feasibility of bilinear matrix inequalities. Then, a new procedure based on LMI optimization and a hybrid algorithm of the particle swarm optimization and differential evolution is used to solve an optimization problem with bilinear matrix inequality constraints. Simulation results show that the designed active suspension system still can guarantee their own performance in spite of the existence of the model uncertainties, the actuator time‐delay and the controller gain variations. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust FOPID controller design for fractional‐order delay systems using positive stability region analysis

In this paper, a robust fractional‐order PID (FOPID) controller design method for fractional‐order delay systems is proposed based on positive stability region (PSR) analysis. Firstly, the PSR is presented to improve the existing stability region (SR) in D‐decomposition method. Then, the optimal fractional orders λ and μ of FOPID controller are achieved at the biggest three‐dimensional PSR, which means the best robustness. Given the optimal λ and μ, the other FOPID controller parameters k_p, k_i, k_d can be solved under the control specifications, including gain crossover frequency, phase margin, and an extended flat phase constraint. In addition, the steps of the proposed robust FOPID controller design process are listed at length, and an example is given to illustrate the corresponding steps. At last, the control performances of the obtained robust FOPID controller are compared with some other controllers (PID and FOPI). The simulation results illustrate the superior robustness as well as the transient performance of the proposed control algorithm.     

Multi‐objective robust fuzzy fractional order proportional–integral–derivative controller design for nonlinear hydraulic turbine governing system using evolutionary computation techniques

The present paper proposes a novel multi‐objective robust fuzzy fractional order proportional–integral–derivative (PID) controller design for nonlinear hydraulic turbine governing system (HTGS) by using evolutionary computation techniques. The fuzzy fractional order PID (FOPID) controller takes closed loop error and its fractional derivative as inputs and performs fuzzy logic operations. Then, it produces the output through the fractional order integrator. The predominant advantages of the proposed controller are its capability to handle complex nonlinear processes like HTGS in heuristic manner, due to fuzzy incorporation and extending an additional flexibility in tuning the order of fractional derivative/integral terms to enhance the closed loop performance. The present work formulates the optimal tuning problem of fuzzy FOPID controller for HTGS as a multi‐objective one instead of a traditional single‐objective one towards satisfying the conflicting criteria such as less settling time and minimum damped oscillations simultaneously to ensure the improved dynamic performance of HTGS. The multi‐objective evolutionary computation techniques such as non‐dominated sorting genetic algorithm‐II (NSGA‐II) and modified NSGA‐II have been utilized to find the optimal input/output scaling factors of the proposed controller along with the order of fractional derivative/integral terms for HTGS system under no load and load turbulence conditions. The performance of the proposed fuzzy FOPID controller is compared with PID and FOPID controllers. The simulations have been conducted to test the tracking capability and robust performance of HTGS during dynamic set point changes for a wide range of operating conditions and model parameter variations, respectively. The proposed robust fuzzy FOPID controller has ensured better fitness value and better time domain specifications than the PID and FOPID controllers, during optimization towards satisfying the conflicting objectives such as less settling time and minimum damped oscillations simultaneously, due to its special inheritance of fuzzy and FOPID properties.     

Stabilization and Tracking Control of X‐Z Inverted Pendulum Using Flatness Based Active Disturbance Rejection Control

A flatness based robust active disturbance rejection control technique scheme with tracking differentiator is proposed for the problem of stabilization and tracking control of the X‐Z inverted pendulum known as a special underactuated, non‐feedback linearizable mechanical system. The differential parameterization on the basis of linearizing the system around an arbitrary equilibrium decouples the underactuated system into two lower order systems, resulting in two lower‐order extended state observers. Using a tracking differentiator to arrange the transient process utilizes the problem of stabilization and tracking control and gives a relatively small initial estimation error, which enlarges the range of the controller parameters. The convincing analysis of the proposed modified linear extended state observer is presented to show its high effectiveness on estimating the states and the extended states known as the total disturbances consisting of the unknown external disturbances and the nonlinearities neglected by the linearization. Simulation results on the stabilization and tracking control of the X‐Z inverted pendulum, including a comparative simulation with an all‐state‐feedback sliding mode controller are presented to show the advantages of the combination of flatness and active disturbance rejection control techniques.     

Reliable control design for composite‐driven scheme based on delay networked T‐S fuzzy system

This paper is focused on reliable controller design for a composite‐driven scheme of networked control systems via Takagi‐Sugeno fuzzy model with probabilistic actuator fault under time‐varying delay. The proposed scheme is distinguished from the other schemes as mentioned in this paper. Aims of this article are to solve the control problem by considering the H_∞, dissipative, and L₂?L_∞ constraints in a unified way. Firstly, to improve the efficient utilization of bandwidth, the adaptive composite‐driven scheme is introduced. In such a scenario, the channel transmission mechanism can be adjusted between adaptive event‐triggered generator scheme and time‐driven scheme. In this study, the threshold is dependent on a new adaptive law, which can be obtained online rather than a predefined constant. With a constant threshold, it is difficult to get the variation of the system. Secondly, a novel fuzzy Lyapunov‐Krasovskii functional is constructed to design the fuzzy controller, and delay‐dependent conditions for stability and performance analysis of the control system are obtained. Then, LMI‐based conditions for the existence of the desired fuzzy controller are presented. Finally, an inverted pendulum that is controlled through the channel is provided to illustrate the effectiveness of the proposed method.     

Sliding mode control of uncertain fractional‐order systems: A reaching phase free approach

This paper proposes a sliding surface which renders the system dynamics to start directly from itself without a reaching phase. More specifically, the system dynamics is insensitive to matched disturbances/uncertainties throughout the entire system response. The controller design based on reduced‐order subsystem is still preserved. It is different from integral sliding mode in which the design is based on the full order of the system to reach the same objective. The simulation results of its application to a fractional inverted pendulum system is demonstrated.     

Fractional Control of a Humanoid Robot Reduced Model with Model Disturbances

There is an open discussion between those who defend mass-distributed models for humanoid robots and those in favor of simple concentrated models. Even though each of them has its advantages and disadvantages, little research has been conducted analyzing the control performance due to the mismatch between the model and the real robot, and how the simplifications affect the controller’s output. In this article we address this problem by combining a reduced model of the humanoid robot, which has an easier mathematical formulation and implementation, with a fractional order controller, which is robust to changes in the model parameters. This controller is a generalization of the well-known proportional–integral–derivative (PID) structure obtained from the application of Fractional Calculus for control, as will be discussed in this article. This control strategy guarantees the robustness of the system, minimizing the effects from the assumption that the robot has a simple mass distribution. The humanoid robot is modeled and identified as a triple inverted pendulum and, using a gain scheduling strategy, the performances of a classical PID controller and a fractional order PID controller are compared, tuning the controller parameters with a genetic algorithm.     

Reliability-based robust Pareto design of linear state feedback controllers using a multi-objective uniform-diversity genetic algorithm (MUGA)

In this paper, fuzzy threshold values, instead of crisp threshold values, have been used for optimal reliability-based multi-objective Pareto design of robust state feedback controllers for a single inverted pendulum having parameters with probabilistic uncertainties. The objective functions that have been considered are, namely, the normalized summation of rising time and overshoot of cart (S_RO–C) and the normalized summation of rising time and overshoot of pendulum (S_RO–P) in the deterministic approach. Accordingly, the probabilities of failure of those objective functions are also considered in the reliability-based design optimization (RBDO) approach. A new multi-objective uniform-diversity genetic algorithm (MUGA) is presented and used for Pareto optimum design of linear state feedback controllers for single inverted pendulum problem. In this way, Pareto front of optimum controllers is first obtained for the nominal deterministic single inverted pendulum using the conflicting objective functions in time domain. Such Pareto front is then obtained for single inverted pendulum having probabilistic uncertainties in its parameters using the statistical moments of those objective functions through a Monte Carlo simulation (MCS) approach. It is shown that multi-objective reliability-based Pareto optimization of the robust state feedback controllers using MUGA with fuzzy threshold values includes those that may be obtained by various crisp threshold values of probability of failures and, thus, remove the difficulty of selecting suitable crisp values. Besides, the multi-objective Pareto optimization of such robust feedback controllers using MUGA unveils some very important and informative trade-offs among those objective functions. Consequently, some optimum robust state feedback controllers can be compromisingly chosen from the Pareto frontiers.     

直线一级倒立摆分数阶控制器设计及仿真

针对直线一级倒立摆的稳定控制问题,设计了分数阶比例积分(FOPI和FO[PI])控制器。首先,根据Newton力学方法建立了倒立摆系统的数学模型。然后,采用基于向量的增益鲁棒性分数阶控制器参数求解简化算法,设计了分数阶比例积分控制器。最后,在MATLAB环境下进行了分数阶比例积分控制器参数整定方法的有效性验证,并且对倒立摆系统分别采用分数阶比例积分控制器和整数阶PID(IOPID)控制器进行了稳定控制仿真实验,并将得到的摆杆角度响应曲线进行了对比分析。结果表明:分数阶比例积分控制器对系统的稳定控制效果优于IOPID控制器,且在分数阶比例积分控制器中,FO[PI]控制器对系统稳定控制最好,响应时间较快、振荡幅值较小且具有鲁棒性。     

Time‐varying feedback for stabilization in prescribed finite time

This paper provides a time‐varying feedback alternative to control of finite‐time systems, which is referred to as “prescribed‐time control,” exhibiting several superior features: (i) such time‐varying gain–based prescribed‐time control is built upon regular state feedback rather than fractional‐power state feedback, thus resulting in smooth (C^m) control action everywhere during the entire operation of the system; (ii) the prescribed‐time control is characterized with uniformly prespecifiable convergence time that can be preassigned as needed within the physically allowable range, making it literally different from not only the traditional finite‐time control (where the finite settling time is determined by a system initial condition and a number of design parameters) but also the fixed‐time control (where the settling time is subject to certain constraints and thus can only be specified within the corresponding range); and (iii) the prescribed‐time control relies only on regular Lyapunov differential inequality instead of fractional Lyapunov differential inequality for stability analysis and thus avoids the difficulty in controller design and stability analysis encountered in the traditional finite‐time control for high‐order systems.     

H∞ Non‐Fragile Synchronous Guaranteed Control of Uncertainty Complex Dynamic Network with Time‐Varying Delay

A kind of H_∞ non‐fragile synchronization guaranteed control method is put forward for a class of uncertain time‐varying delay complex network systems with disturbance input. The network under consideration includes unknown but bounded nonlinear coupling functions f(x) and the coupling term and node system with time‐varying delays. The nonlinear vector function f(x) need not be differentiable but should satisfy the norm bound. A non‐fragile state feedback controller of the gain with sufficiently large regulation margin is designed. It is ensured that the parameters of the controller could still be effective under small perturbation. The sufficient conditions for the existence of H_∞ synchronous non‐fragile guaranteed control of this system have been obtained by constructing a suitable Lyapunov‐Krasovskii functional, adopting matrix analysis, using the theorem of Schur complement and linear matrix inequalities (LMI). These conditions can guarantee robust asymptotic stability for each node of network with disturbance as well as achieve a prescribed robust H_∞ performance level. Finally, the feasibility of the designed method is verified by a numerical example.     

Fractional‐order–dependent global stability analysis and observer‐based synthesis for a class of nonlinear fractional‐order systems

This paper focuses on proposing novel conditions for stability analysis and stabilization of the class of nonlinear fractional‐order systems. First, by considering the class of nonlinear fractional‐order systems as a feedback interconnection system and applying small‐gain theorem, a condition is proposed for L₂‐norm boundedness of the solutions of these systems. Then, by using the Mittag‐Leffler function properties, we show that satisfaction of the proposed condition proves the global asymptotic stability of the class of nonlinear fractional‐order systems with fractional order lying in (0.5, 1) or (1.5, 2). Unlike the Lyapunov‐based methods for stability analysis of fractional‐order systems, the new condition depends on the fractional order of the system. Moreover, it is related to the H_∞‐norm of the linear part of the system and it can be transformed to linear matrix inequalities (LMIs) using fractional‐order bounded‐real lemma. Furthermore, the proposed stability analysis method is extended to the state‐feedback and observer‐based controller design for the class of nonlinear fractional‐order systems based on solving some LMIs. In the observer‐based stabilization problem, we prove that the separation principle holds using our method and one can find the observer gain and pseudostate‐feedback gain in two separate steps. Finally, three numerical examples are provided to demonstrate the advantage of the novel proposed conditions with the previous results.     

Robust nonlinear ship course‐keeping control by H∞ I/O linearization and μ‐synthesis

In this paper, the H_∞ input/output (I/O) linearization formulation is applied to design an inner‐loop nonlinear controller for a nonlinear ship course‐keeping control problem. Due to the ship motion dynamics are non‐minimum phase, it is impossible to use the ordinary feedback I/O linearization to resolve. Hence, the technique of H_∞ I/O linearization is proposed to obtain a nonlinear H_∞ controller such that the compensated nonlinear system approximates the linear reference model in I/O behaviour. Then a μ‐synthesis method is employed to design an outer‐loop robust controller to address tracking, regulation, and robustness issues. The time responses of the tracking signals for the closed‐loop system reveal that the overall robust nonlinear controller is able to provide robust stability and robust performance for the plant uncertainties and state measurement errors. Copyright © 2002 John Wiley & Sons, Ltd.     

The Design of a Coprime‐Factorized Predictive Functional Controller for Unstable Fractional Order Systems

In this paper, a new approach, called coprime‐factorized predictive functional control method (CFPFC‐F) is proposed to control unstable fractional order linear time invariant systems. To design the controller, first, a prediction model should be synthesized. For this purpose, coprime‐factorized representation is extended for unstable fractional order systems via a reduced approximated model of unstable fractional order (FO) system. That is, an approximated integer model of fractional order system is derived via the well‐known Oustaloup method. Then, the high order approximated model is reduced to a lower one via a balanced truncation model order reduction method. Next, the equivalent coprime‐factorized model of the unstable fractional‐order plant is employed to predict the output of the system. Then, a predictive functional controller (PFC) is designed to control the unstable plant. Finally, the robust stability of the closed‐loop system is analyzed via small gain theorem. The performance of the proposed control is investigated via simulations for the control of an unstable non‐laminated electromagnetic suspension system as our simulation test system.     

Robust fuzzy control for continuous perturbed time‐delay affine takagi–sugeno fuzzy models

The stability analysis and controller synthesis methodology for a continuous perturbed time‐delay affine (CPTDA) Takagi–Sugeno (T‐S) fuzzy model is proposed in this paper. The CPTDA T‐S fuzzy models include both linear nominal parts and uncertain parameters in each fuzzy rule. The proposed fuzzy control approach is developed based on an iterative linear matrix inequality (ILMI) algorithm to cope with the stability criteria and H_∞ performance constraints for the CPTDA T‐S fuzzy models. Finally, a numerical simulation for the nonlinear inverted pendulum system is given to show the application and availability of the present design approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

倒立摆系统的变结构控制方案

对单级倒立摆系统的稳定和鲁棒控制问题,提出了一种基于李雅普诺夫直接法的变结构控制方案,理论分析和计算机模拟都表明该控制方案不仅能镇定倒立摆,实现对台车的位移控制,而且当系统参数变化时也实现了对该系统的鲁棒控制.     

A simple model matching for the stabilization of an inverted pendulum cart system

We present a simple model matching controller for the stabilization of the inverted pendulum cart system, assuming that the pendulum is initialized above the horizontal plane. The control strategy consists of forcing the closed‐loop system to behave as another nonlinear target system with some stability properties. To this end, we solve two matching conditions that allow us to shape a suitable target system. Having satisfied both matching conditions, the stabilizing controller is directly obtained from the proposed target system. The obtained close‐loop system is locally asymptotically exponentially stable, with a very large domain of attraction. Copyright © 2007 John Wiley & Sons, Ltd.