Composite fuzzy sliding mode control of nonlinear singularly perturbed systems

This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller.     

Robust observer-based absolute stabilization for Lur’e singularly perturbed systems with state delay

This paper is concerned with the problem of robust observer-based absolute stabilization for Lur’e singularly perturbed time-delay systems. The aim is to design a suitable observer-based feedback control law such that the resulting closed-loop system is absolutely stable. First, a full-order state observer is constructed. Based on the linear matrix inequality (LMI) technique, a delay-dependent sufficient condition is presented such that the observer error system is absolutely stable. Then, for observer-based feedback control, by introducing some slack matrices, a sufficient condition for input-to-state stability (ISS) of the closed-loop system with regard to the observer error is presented. Thus, the absolute stabilization of the closed-loop system can be guaranteed based on the ISS property. In addition, the criteria presented are both independent of the small parameter and the upper bound for the absolute stability can be obtained in a workable algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the developed methods.     

Stabilization of an axially moving accelerated/decelerated system via an adaptive boundary control

In this study, an adaptive boundary control is developed for vibration suppression of an axially moving accelerated/decelerated belt system. The dynamic model of the belt system is represented by partial-ordinary differential equations with consideration of the high acceleration/deceleration and unknown distributed disturbance. By utilizing adaptive technique and Lyapunov-based back stepping method, an adaptive boundary control is proposed for vibration suppression of the belt system, a disturbance observer is introduced to attenuate the effects of unknown boundary disturbance, the adaptive law is developed to handle parametric uncertainties and the S-curve acceleration/deceleration method is adopted to plan the belt׳s speed. With the proposed control scheme, the well-posedness and stability of the closed-loop system are mathematically demonstrated. Simulations are displayed to illustrate the effectiveness of the proposed control.     

Nonlinear gearshifts control of dual-clutch transmissions during inertia phase

In this paper, a model-based nonlinear gearshift controller is designed by the backstepping method to improve the shift quality of vehicles with a dual-clutch transmission (DCT). Considering easy-implementation, the controller is rearranged into a concise structure which contains a feedforward control and a feedback control. Then, robustness of the closed-loop error system is discussed in the framework of the input to state stability (ISS) theory, where model uncertainties are considered as the additive disturbance inputs. Furthermore, due to the application of the backstepping method, the closed-loop error system is ordered as a linear system. Using the linear system theory, a guideline for selecting the controller parameters is deduced which could reduce the workload of parameters tuning. Finally, simulation results and Hardware in the Loop (HiL) simulation are presented to validate the effectiveness of the designed controller.     

An energy-saving nonlinear position control strategy for electro-hydraulic servo systems

The electro-hydraulic servo system (EHSS) demonstrates numerous advantages in size and performance compared to other actuation methods. Oftentimes, its utilization in industrial and machinery settings is limited by its inferior efficiency. In this paper, a nonlinear backstepping control algorithm with an energy-saving approach is proposed for position control in the EHSS. To achieve improved efficiency, two control valves including a proportional directional valve (PDV) and a proportional relief valve (PRV) are used to achieve the control objectives. To design the control algorithm, the state space model equations of the system are transformed to their normal form and the control law through the PDV is designed using a backstepping approach for position tracking. Then, another nonlinear set of laws is derived to achieve energy-saving through the PRV input. This control design method, based on the normal form representation, imposes internal dynamics on the closed-loop system. The stability of the internal dynamics is analyzed in special cases of operation. Experimental results verify that both tracking and energy-saving objectives are satisfied for the closed-loop system.     

基于微分平坦的旋转倒立摆双闭环抗扰 PID 控制

针对一类不稳定、欠驱动二自由度旋转倒立摆系统, 提出一种基于微分平坦的双闭环抗扰 PID 控制方法。 首先, 建立倒 立摆的非线性动力学模型, 利用近似线性化分析系统的不稳定零动态与非最小相位特性; 然后, 结合微分平坦理论, 设计倒立摆 平坦输出,重构系统平坦状态, 并建立平坦状态与角度输出之间的转化关系,克服倒立摆的非最小相位影响; 进一步, 针对微分 平坦系统, 设计抗扰 PID 双闭环控制结构和带宽化调节方法, 在主动抗扰机制下实现对摆杆角度与悬臂角度的精准控制; 最后, 通过仿真与实验, 验证所提方法的有效性和实用性。 所提方法为欠驱动系统提供了一种结构简单、抗扰能力强的控制方案。     

Synthesis of feedback control elements for discrete event systems using Petri net models and theory of regions

This paper describes a method for constructing a Petri-net-based controller for a discrete event system (DES) modelled by a Petri net. Assuming that an uncontrolled Petri net model of the DES and a set of forbidden state specifications are given, feedback control elements, i.e. a set of places and related transitions, with initial marking, are computed using the theory of regions, which is a formal synthesis technique for deriving Petri nets from automaton-based models. When feedback control elements are added to the uncontrolled Petri net model, the controlled (closed-loop) Petri net model of the system is obtained. The controlled Petri net model obtained is maximally permissive while guaranteeing that forbidden states do not occur. The proposed method is computationally efficient and does not suffer from the state explosion problem. Two examples are provided to show the applicability of the proposed method.     

具有状态约束的电液伺服系统模型参考鲁棒自适应控制

针对电液伺服系统中的模型不确定性和状态约束问题,设计了一种模型参考鲁棒自适应控制(MRRAC)方法。将电液伺服系统的近似模型作为模型预测控制(MPC)的设计对象,在设计过程中考虑状态约束,并生成受约束的状态期望,作为后续伺服控制方法的参考指令。为了克服液压系统中的模型不确定性,基于反步法设计了鲁棒自适应控制器(RAC),实现了兼顾模型不确定性和状态约束的伺服控制。基于Lyapunov稳定性理论证明了所设计控制策略的闭环渐近稳定性,且系统所有信号均有界。仿真结果表明,控制器对于系统模型不确定性具有较强的鲁棒性,且可实现对指定状态的有效约束,充分验证了该控制策略的有效性。     

Output feedback boundary control of an axially moving system with input saturation constraint

This paper is concerned with boundary control for an axially moving belt system with high acceleration/deceleration subject to the input saturation constraint. The dynamics of belt system is expressed by a nonhomogeneous hyperbolic partial differential equation coupled with an ordinary differential equation. First, state feedback boundary control is designed for the case that the boundary states of the belt system can be measured. Subsequently, output feedback boundary control is developed when some of the system states can not be accurately obtained. The well-posedness and the uniformly bounded stability of the closed-loop system are achieved through rigorous mathematical analysis. In addition, high-gain observers are utilized to estimate those unmeasurable states, the auxiliary system is introduced to eliminate the constraint effects of the input saturation, and the disturbance observer is adopted to cope with unknown boundary disturbance. Finally, the control performance of the belt system is illustrated by carrying out numerical simulations.     

Constrained off-line synthesis approach of model predictive control for networked control systems with network-induced delays

This paper investigates the off-line synthesis approach of model predictive control (MPC) for a class of networked control systems (NCSs) with network-induced delays. A new augmented model which can be readily applied to time-varying control law, is proposed to describe the NCS where bounded deterministic network-induced delays may occur in both sensor to controller (S–A) and controller to actuator (C–A) links. Based on this augmented model, a sufficient condition of the closed-loop stability is derived by applying the Lyapunov method. The off-line synthesis approach of model predictive control is addressed using the stability results of the system, which explicitly considers the satisfaction of input and state constraints. Numerical example is given to illustrate the effectiveness of the proposed method.     

阀控液压伺服系统的辨识与优化设计研究

根据阀控缸电液位置伺服系统的组成,对系统中的阀控缸的数学模型进行了研究,并通过系统辨识的方法得到了阀控缸系统的闭环传递函数,控制器采用全维状态反馈,以二阶工程最佳为优化目标建立了系统的仿真模型。仿真结果表明该控制器实现了液压位置伺服系统的极点配置,完成了优化目标。表明全状态反馈控制能够提高液压伺服系统的位置跟踪精度,具有工程可行性。     

A hybrid approach to supervisory control of discrete event systems coupling RW supervisors to Petri nets

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.     

Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: A new optimization approach

The partial quadratic eigenvalue assignment problem (PQEVAP) concerns reassigning a few undesired eigenvalues of a quadratic matrix pencil to suitably chosen locations and keeping the other large number of eigenvalues and eigenvectors unchanged (no spill-over). The problem naturally arises in controlling dangerous vibrations in structures by means of active feedback control design. For practical viability, the design must be robust, which requires that the norms of the feedback matrices and the condition number of the closed-loop eigenvectors are as small as possible. The problem of computing feedback matrices that satisfy the above two practical requirements is known as the Robust Partial Quadratic Eigenvalue Assignment Problem (RPQEVAP). In this paper, we formulate the RPQEVAP as an unconstrained minimization problem with the cost function involving the condition number of the closed-loop eigenvector matrix and two feedback norms. Since only a small number of eigenvalues of the open-loop quadratic pencil are computable using the state-of-the-art matrix computational techniques and/or measurable in a vibration laboratory, it is imperative that the problem is solved using these small number of eigenvalues and the corresponding eigenvectors. To this end, a class of the feedback matrices are obtained in parametric form, parameterized by a single parametric matrix, and the cost function and the required gradient formulas for the optimization problem are developed in terms of the small number of eigenvalues that are reassigned and their corresponding eigenvectors. The problem is solved directly in quadratic setting without transforming it to a standard first-order control problem and most importantly, the significant “no spill-over property” of the closed-loop eigenvalues and eigenvectors is established by means of a mathematical result. These features make the proposed method practically applicable even for very large structures. Results on numerical experiments show that the proposed method considerably reduces both feedback norms and the sensitivity of the closed-loop eigenvalues. A study on robustness of the system responses of the method under small perturbations show that the responses of the perturbed closed-loop system are compatible with perturbations.     

Robust observer-based OMF vibration control of flexible linkage mechanisms using piezoelectric films

Based on the state-space model of the flexible linkage mechanism equipped with piezoelectric films, a robust control methodology for actively suppressing the elastodynamic responses of the high-speed flexible linkage mechanism with linear structured time-varying parameter perturbations by employing an observer-based optimal model-following (OMF) controller is presented. The advantage of the proposed robust observer-based OMF control methodology is that it not only can avoid the problem of how to choose the appropriate weighting matrices in the quadratic cost function of the linear-quadratic/linear-quadratic-Gaussian (LQ/LQG) control method but also can make the controlled closed-loop system to have the specified system response characteristics. Besides, in order to guarantee that the designed observer-based OMF controller can make the controlled flexible linkage mechanism system to avoid the possibilities of both spillover-induced instability and time-varying-parameter-perturbation-induced instability, a robust stability criterion is also presented in this paper. The control method, presented in this paper, can not only make the controlled closed-loop system to have the specified system response characteristics, but also guarantee the controlled closed-loop system to have robust stability properties by using the proposed robust stability criterion; while those control methods reported recently do not have these above-mentioned merits. Finally, an active robust vibration control problem of a slider-crank mechanism is provided for illustrating the applicability of the proposed method.     

One-step receding horizon H(∞) control for networked control systems with random delay and packet disordering

The receding horizon H(∞) control (RHHC) problem is investigated in this paper for a class of networked control systems (NCSs) with random delay and packet disordering. A new model is proposed to describe the NCS with random delay which may be larger than one sampling period. The random delay is modeled as a Markov chain while the closed-loop system is described as a Markovian jump system. Sufficient conditions for the closed-loop NCS to be stochastically stable and the performance index to be upper bounded are derived by using the receding optimization principle. Furthermore, by solving a semi-definite programming (SDP) with linear matrix inequalities (LMIs) constraint, a piecewise-constant receding horizon H(∞) controller is obtained, and the designed piecewise-constant controller ensures that the closed-loop NCS achieves a prescribed H(∞) disturbance attenuation level. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.     

Modeling and distributed gain scheduling strategy for load frequency control in smart grids with communication topology changes

In this paper, we investigate the modeling and distributed control problems for the load frequency control (LFC) in a smart grid. In contrast with existing works, we consider more practical and real scenarios, where the communication topology of the smart grid changes because of either link failures or packet losses. These topology changes are modeled as a time-varying communication topology matrix. By using this matrix, a new closed-loop power system model is proposed to integrate the communication topology changes into the dynamics of a physical power system. The globally asymptotical stability of this closed-loop power system is analyzed. A distributed gain scheduling LFC strategy is proposed to compensate for the potential degradation of dynamic performance (mean square errors of state vectors) of the power system under communication topology changes. In comparison to conventional centralized control approaches, the proposed method can improve the robustness of the smart grid to the variation of the communication network as well as to reduce computation load. Simulation results show that the proposed distributed gain scheduling approach is capable to improve the robustness of the smart grid to communication topology changes.     

Generalized predictor based active disturbance rejection control for non-minimum phase systems

In this paper, a generalized predictor based control scheme is proposed to improve system performance of set-point tracking and disturbance rejection for non-minimum phase (NMP) systems. By using a generalized predictor to estimate the system output without time delay, a model-based extended state observer (MESO) is designed to simultaneously estimate the system state and disturbance. Accordingly, an active disturbance rejection control design is developed which consists of a state feedback control and a feedforward control for the disturbance rejection. The MESO and feedback controllers are analytically derived by specifying the desired characteristic roots of MESO and closed-loop system poles, respectively. To improve the output tracking performance, a pre-filter is designed based on a desired closed-loop transfer function for the set-point tracking. A sufficient condition guaranteeing robust stability of the closed-loop system against time-varying uncertainties is established in terms of linear matrix inequalities (LMIs). Three illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control scheme.     

Robust covariance control for discrete system by Takagi-Sugeno fuzzy controllers

Variances of the system states or outputs often play vital roles in the problem for performance requirements of many stochastic control systems. For linear stochastic systems, the covariance control technique has been applied to deal with the variance constrained design problem. This paper extends this technique to a class of discrete-time nonlinear perturbed stochastic systems, which are modeled by the Takagi-Sugeno (TS) fuzzy systems. By fuzzy IF-THEN rules, which represent local linear input-output relations, the nonlinear systems can be described by TS fuzzy models. According to the parallel distributed compensation (PDC) concept, the discrete-time nonlinear perturbed stochastic systems can be driven by the linear feedback gains. The purpose of this paper is to provide a method to design an output feedback fuzzy controller, which is based on the upper bound state covariance control technique and PDC concept, for the discrete-time perturbed stochastic systems using TS fuzzy models.     

Sampled-data-based vibration control for structural systems with finite-time state constraint and sensor outage

The problem of sampled-data-based vibration control for structural systems with finite-time state constraint and sensor outage is investigated in this paper. The objective of designing controllers is to guarantee the stability and anti-disturbance performance of the closed-loop systems while some sensor outages happen. Firstly, based on matrix transformation, the state-space model of structural systems with sensor outages and uncertainties appearing in the mass, damping and stiffness matrices is established. Secondly, by considering most of those earthquakes or strong winds happen in a very short time, and it is often the peak values make the structures damaged, the finite-time stability analysis method is introduced to constrain the state responses in a given time interval, and the H-infinity stability is adopted in the controller design to make sure that the closed-loop system has a prescribed level of disturbance attenuation performance during the whole control process. Furthermore, all stabilization conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using the LMI Toolbox. Finally, numerical examples are given to demonstrate the effectiveness of the proposed theorems.     

具有状态约束的机械臂切换自适应控制

为了解决具有状态约束的机械臂的控制问题,本文针对一类具有全状态约束和状态不完全可测的切换严格反馈非线性系统进行研究,通过引入状态观测器、自适应神经网络和动态表面控制技术,设计了一种基于径向基函数(RBF)神经网络的自适应输出反馈控制方法。利用Lyapunov方法和平均驻留时间理论(ADT)保证了闭环系统所有信号是半全局一致最终有界的(SGUUB),通过数值例子仿真验证了所提方法的有效性。最后将该方法应用于带电机驱动的机械臂并进行仿真实验,仿真结果表明,机械臂轨迹跟踪误差很小,有着良好的控制精度,同时也表明所提出的控制算法能够应用于实际工程模型。