Actuator fault tolerance based on continuous-time fuzzy singularly perturbed model

Actuator fault tolerance based on fuzzy singularly perturbed model (FSPM) for nonlinear singularly perturbed systems (NSPSs) is investigated. A continuous-time FSPM with subtractive faults on control input is presented to describe NSPSs with actuator faults, which is less conservative than slow–fast submodel methods. A hybrid fuzzy controller (HFC) consisting of a fuzzy detector and a fault-tolerant controller can realize real-time fault tolerance, such that the target system with actuator faults is stabilized. The theorem to solve controller gains is derived by using Lyapunov, singular perturbation, $H_{\infty }$, and Schur complement theories, which can avoid the problem that the feasible solutions cannot be obtained by solving linear matrix inequalities (LMIs). A nonlinear item was replaced by a linear item, which provides a good idea for solving nonlinear matrix inequalities. The sudden and remittent actuator faults of a motor system are suppressed by using the above approaches.     

Multi-objective robust control based on fuzzy singularly perturbed models for hypersonic vehicles

In this paper, we propose a multi-objective robust controller based on fuzzy singularly perturbed models (FSPM) for the longitudinal motion of an air-breathing hypersonic vehicle. The control objective is to provide velocity and altitude tracking in the presence of the uncertainties and unknown nonlinearities in the model caused by variations in flight conditions. By approximating the multi-time-scale model with FSPM, ill-posed matrix calculations are circumvented. Under this framework, a fuzzy multi-object...     

磁通切换型定子永磁电机的建模与线性自抗扰控制

磁通切换型永磁（FSPM）电机是一种新型的定子永磁型无刷电机,在制造业及航海等领域具有很好的应用前景。FSPM电机的高性能控制具有很大的难度。在分析这种电机工作原理的基础上,建立了其在定子坐标系和转子旋转坐标系下的数学模型。采用电流滞环的PWM控制策略,并将线性自抗扰控制器（LADRC）引入到其调速系统中。稳态和动态仿真结果表明,采用LADRC的磁通切换永磁电机比采用PI控制的调速系统具有更好的启动特性,并在转速突变和突加负载扰动时具有更强的鲁棒性。     

Asymptotic stabilization of high‐order feedforward systems with delays in the input

This paper deals with the state feedback controller design for a class of high‐order feedforward (upper‐triangular) nonlinear systems with delayed inputs. The uncertainties in the systems are assumed to be dominated by higher‐order nonlinearities multiplying by a constant growth rate. The designed controller, which is a continuous but not smooth feedback, could achieve global asymptotical stability. Based on the appropriate state transformation of time‐delay systems, the problem of controller design can be converted into the problem of finding a parameter, which can be obtained by appraising the nonlinear terms of the systems. The nonlinear systems considered here are more general than conventional feedforward systems and they could be viewed as generalized feedforward systems. Two examples are given to show the effectiveness of the proposed design procedure. Copyright © 2009 John Wiley & Sons, Ltd.     

Design of a nonlinear controller based on a piecewise-linear Hammerstein model

This paper presents a nonlinear controller, which can be used to control single-input single-output nonlinear systems that can be approximated in terms of Hammerstein models. The proposed nonlinear controller is based on the principles of a classic linear pole placement controller and the piecewise-linear Hammerstein model. The controller can be used to control processes with highly nonlinear or even discontinuous static functions, while keeping simple controller structure and a very low computational burden.     

一类混沌系统的状态观测与控制

基于混沌系统运动的有界性,使得不依赖于对象模型的扩张状态观测器可用于一类混沌系统的状态观测。只要扩张状态观测器充分观测到混沌系统的状态,自抗扰控制器就可以控制混沌系统,几个混沌数值仿真表明了扩张状态观测器和自抗扰控制器可有效地用于混沌系统的观测和控制。     

Time-scale separation and robust controller design for uncertain nonlinear singularly perturbed systems under perfect state measurements

We study time-scale separation and robust controller design for a class of singularly perturbed nonlinear systems under perfect state measurements. The system dynamics are taken to be jointly linear in the fast state variables, control and disturbance inputs, but nonlinear in the slow state variables. Since global timescale separation may not always be possible for nonlinear singularly perturbed systems, we restrict our attention here to some closed subset of the state space, on which a timescale separation holds for sufficiently small values of the singular perturbation parameter. We construct a slow controller and a composite controller based on the solutions of particular slow and fast games obtained using time-scale separation. For the class of systems for which the slow controller can be selected to be robust with respect to small regular structural perturbations on the slow subsystem, we show under some growth conditions that the composite controller can achieve any desired level of performance that is larger than the maximum of the performance levels for the slow and fast subsystems,. A slow controller, however, is not generally as robust as the composite controller; but, still under some conditions which are delineated in the paper, the fast dynamics can be totally ignored. The paper also presents a numerical example to illustrate the theoretical results.     

Synchronisation control of composite chaotic systems

Synchronisation conditions are studied for composite chaotic systems with complex compound structure and the signum function based on the theorem of zero-solution stability for a class of linear time-varying systems with countable discontinuous points. The synchronisation controller and its gain range are deduced according to the stability theorem, where the gain of the controller can speed synchronisation. Numerical simulation further proves the control theory and the validity of the synchronisation controller. The proposed controller can be widely applied in those chaotic systems with switch functions or other hybrid chaotic systems.     

Robust control of the electrostatic torsional micromirrors

In order to simplify the sensors subsystems of the electrostatic torsional micromirrors (ETMs), the output feedback control for the ETM systems is investigated in this paper. The dynamics of the systems is established by combining the dynamics of both the mechanical and electronic subsystems, and it is proved that the dynamics of the overall system with uncertainties in electrical parameters can be exactly transformed into the third order linear system. Then an output feedback finite-time stabilizing (FTS) controller is presented by composing of a full state FTS observer and a state feedback FTS controller for the third order linear systems, such that the ETM systems can be stabilized in its full travel range by merely measuring the tilt angle. Some numerical simulations demonstrate the stability of the proposed output feedback FTS controller.     

视故障为结构不确定项的鲁棒可靠跟踪控制器设计

针对含执行机构故障的凸面体不确定系统, 本文基于二次型分离算子给出了一种鲁棒可靠跟踪控制器的设计方法. 利用不确定系统鲁棒镇定时的拓扑分离特性, 采用无损S-procedure获得二次型分离算子, 对执行机构故障和系统描述矩阵进行解耦, 在此基础上将故障模型的结构信息引入到控制器设计中, 从而减少系统设计的保守性. 并将可靠控制器设计转化为线性矩阵不等式表述的凸优化问题, 利用已有的工具包对其快速求解. 最后给出某飞行器纵向运动控制的设计实例, 仿真结果验证了设计方法的有效性和优越性.     

一类不确定动态时滞系统的无记忆鲁棒镇定控制

针对状态和控制均存在滞后,同时具有未知且有界的一类时变不确定线性时滞系 统,提出了一种无记忆鲁棒镇定控制器设计算法.给出了闭环系统二次稳定的充分条件,并利 用一等价线性时不变系统的H∞标准问题综合方法来构造出所需的线性状态反馈控制律,即 可通过求解一代数Riccati型方程来求得控制律静态增益阵,从而保证了解的存在性和可解 性.     

非线性大系统的分散线性化与分散控制

将非线性控制系统的精确线性化方法应用于非线性大系统,提出了非线性大系统 的分散线性化方法,并得到了非线性系统可分散线性化的充要条件.按照这个方法,可将难度 较大的一类非线性大系统分散控制器的设计转化为易于处理的线性大系统分散控制器的设 计.在得到该线性大系统的分散控制器后,可通过分散坐标变换的逆变换将线性大系统的控 制器变换为原非线性大系统的控制器.同时,控制器的分散性保持不变.该方法明显地降低了 该类非线性大系统分散控制器的设计难度.     

Lyapunov functions and the control of the Euler-Bernoulli beam

A controller for the Euler-Bernoulli beam is derived using the complete distributed model along with a Lyapunov function approach. Model structure is therefore preserved in the control law whose parameters can be used to balance two different types of behaviour: the gross motion of the beam and the vibration superimposed on it. In the limiting case of a rigid beam, these two types of behaviour become indistinguishable and so the controller reduces to a proportional feedback law. This approach also guarantees that the controller provides asymptotic trajectory tracking for smooth initial conditions. Also, since it is not constrained to linear systems it could, in principle, be used for multi-link flexible robot systems.     

一类三维动力系统的同步控制与仿真

针对一类三维动力系统,提出了一种同步控制法。基于李雅谱诺夫稳定性理论设计了一简单的自适应反馈控制器来实现同步控制。理论证明和数值模拟的结果都验证了控制器的有效性。控制器简单便于实现,更可以用于一般非线性混沌系统的控制。     

Precise control of the pressure-driven flows considering the pressure fluctuations induced by the process of droplet formation

The pressure-driven device is designed to control the flow rates of the droplet microfluidic systems, which can significantly reduce the flow-rate fluctuations coming from the pump source. As monodisperse droplets are formed in the microchannel, periodic pressure fluctuations can be induced by the dynamic process of droplet formation, which can influence the stability and control precision of the pressure-driven flows. The effects of the pressure fluctuations induced by the droplet formation process on the dynamic characteristics of the open-loop and closed-loop control pressure-driven devices are comparatively studied. Particularly, a proportional–integral controller (PI controller) is integrated with the closed-loop control pressure-driven device and the effects of the PI controller parameters on the stability and control accuracy of the pressure-driven flows are tested experimentally. Particularly, by properly choosing the parameters of the PI controller, the magnitude of the periodic pressure fluctuations can be reduced drastically, which obviously increases the control precision of the pressure-driven flows.     

On the stability of linear time-varying feedback systems with random parameters

The problem of finding frequency-domain conditions which guarantee asymptotic stability with probability 1 of linear systems with a time-varying feedback controller and having white noise parameter variations is considered. It is shown that the stochastic version of the second method of Liapunov can be employed for deriving sufficient conditions for stability of such systems. Stability criteria are derived after taking into account restrictions on the gain as well as on the rate of change of the gain of the controller.     

A neural gain scheduling network controller for nonholonomicsystems

We propose a neural gain scheduling network controller (NGSNC) to improve the gain scheduling controller for nonholonomic systems. We derive the neural networks that can approximate the gain scheduling controller arbitrarily well when the sampling frequency satisfies the sampling theorem. We also show that the NGSNC is independent of the sampling time. The proposed NGSNC has the following important properties: 1) same performance as the continuous-parameter gain scheduling controller; 2) less computing time than the continuous-parameter gain scheduling controller; 3) good robustness against the sampling intervals; and 4) straightforward stability analysis. We then show that some of nonholonomic systems can be converted to equivalent linear parameter-varying systems. As a result, the NGSNC can stabilize nonholonomic systems     

Chaos synchronization of nonlinear gyros using self-learning PID control approach

Since chaotic systems are important nonlinear deterministic systems that display complex, noisy-like and unpredictable behavior, synchronizing chaotic systems has become an important issue in the engineering community. Due to the proportional-integral-derivative (PID) controller has a simple architecture and easily designed, it was widely used in the industrial applications. However, the traditional PID controller usually needs some manual retuning before being used to practically application. To tackle this problem, this paper proposes a self-learning PID control (SLPIDC) system which is composed of a PID controller and a fuzzy compensator. The PID controller which is used to online approximate an ideal controller is the main controller. The controller gain factors of the PID controller can automatically tune based on the gradient descent method. The fuzzy compensator is designed to dispel the approximation error between the ideal controller and PID controller upon the system stability in the Lyapunov sense. From the simulation results, it is verified that the chaotic behavior of two nonlinear identical chaotic gyros can be synchronized by the proposed SLPIDC scheme without the chattering phenomena in the control effort after the controller parameters learning.     

Global asymptotic stabilization of feedforward nonlinear systems with a delay in the input

In this paper, by constructing appropriate Lyapunov–Krasovskii functionals (LKF) and applying the model transformation of time-delay systems, a design scheme of state feedback controller for a class of feedforward nonlinear systems with a delay in the input is proposed. The designed controllers have a very simple structure and do not involve any saturation or recursive computation, which is widely applied in designing a controller of feedforward nonlinear systems. Using the transformation of coordinates and the property of Hurwitz polynomial, the problem of designing controller can be converted into the problem of finding a parameter, which can be solved by solving the optimization problem with linear matrix inequalities (LMIs) constraints. A simulation example is given to show the effectiveness of the proposed design procedure.     

Hybrid fuzzy control of robotics systems

This paper presents a new approach towards optimal design of a hybrid fuzzy controller for robotics systems. The salient feature of the proposed approach is that it combines the fuzzy gain scheduling method and a fuzzy proportional-integral-derivative (PID) controller to solve the nonlinear control problem. The resultant fuzzy rule base of the proposed controller can be decomposed into two layers. In the upper layer, the gain scheduling method is incorporated with a Takagi-Sugeno (TS) fuzzy logic controller to linearize the robotics system for a given reference trajectory. In the lower layer, a fuzzy PID controller is derived for all the locally linearized systems by replacing the conventional PI controller by a linear fuzzy logic controller, which has different gains for different linearization conditions. Within the guaranteed stability region, the controller gains can be optimally tuned by genetic algorithms. Simulation studies on a pole balancing robot and a multilink robot manipulator demonstrate the effectiveness and robustness of the proposed approach.