Global optimal fuzzy tracker design based on local concept approach

In this paper, we propose a global optimal fuzzy tracking controller, implemented by fuzzily blending the individual local fuzzy tracking laws, for continuous and discrete-time fuzzy systems with the aim of solving, respectively, the continuous and discrete-time quadratic tracking problems with moving or model-following targets under finite or infinite horizon (time). The differential or recursive Riccati equations, and more, the differential or difference equations in tracing the variation of the target, are derived. Moreover, in the case of time-invariant fuzzy tracking systems, we show that the optimal tracking controller can be obtained by just solving algebraic Riccati equations and algebraic matrix equations. Grounding on this, several fascinating characteristics of the resultant closed-loop continuous or discrete time-invariant fuzzy tracking systems can be elicited easily. The stability of both closed-loop fuzzy tracking systems can be ensured by the designed optimal fuzzy tracking controllers. The optimal closed-loop fuzzy tracking systems cannot only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Moreover, the resulting closed-loop fuzzy tracking systems possess infinite gain margin; that is, their stability is guaranteed no matter how large the feedback gain becomes. Two examples are given to illustrate the performance of the proposed optimal fuzzy tracker design schemes and to demonstrate the proved stability properties     

Approximate local output regulation for nonlinear distributed parameter systems

Output regulation for a class of nonlinear infinite-dimensional systems, called regular nonlinear systems (RNS), is the subject of this work. For the plants in this class, the linearization at the origin is an exponentially stable regular linear system (RLS). The plants are driven by a control input and a disturbance signal. Well-posedness of the plants for small initial states, control inputs and disturbance signals is established and it is shown that if the control input and the disturbance signal for a plant are T-periodic, then so are its state and output (asymptotically). On the basis of this characterization, an approximate local output regulator problem for multi-input multi-output (MIMO) plants in the RNS class is addressed. Given a plant, the regulation objective is to ensure that a finite number of harmonics of a T-periodic reference signal and the plant output are identical whenever the reference signal, the T-periodic disturbance signal for this plant and the initial state are small. An internal model based output feedback control scheme is proposed for an exponentially stable RLS for tracking reference signals, which are a finite sum of functions that are a product of a sinusoid and a polynomial in time. This scheme merely uses the transfer function gains of the RLS at the poles of the Laplace transform of the reference signal and practically requires no other data. Using the proposed control scheme, a linear finite-dimensional controller is designed for a MIMO nonlinear plant in the RNS class using minimal plant information. The resulting closed-loop system is rigorously analyzed to establish that the controller achieves the regulation objective. The efficacy of the control design is illustrated numerically using the model of a cable coupled to a point mass via a nonlinear spring.     

Direct pole placement adaptive tracking of non-minimum phase systems

In this paper, we propose a direct pole placement adaptive tracking scheme for non-minimum-phase, open-loop stable, linear plants with time delays. This controller utilizes the internal model principle to eliminate steady-state tracking error for signals with known distinct frequencies. The controller order depends only on the number of frequencies in the reference input, but not on the order of the plant. It is shown that with sufficiently small loop gain, the controller can guarantee stable closed loop, and asymptotic tracking.     

Output regulation of nonaffine nonlinear systems using singular perturbation theory

A control synthesis method for output regulation based on singular perturbation theory combined with inverting design is considered for a class of nonaffine nonlinear systems. The resulting control signal is defined as a solution to ＂fast＂ dynamics which inverts a series error model, whose state is exponentially stable. It is shown that, under sufficient conditions being consistent with the assumptions of singular perturbation theory, this problem is solvable with （ε） tracking error if and only if a set of first-order nonlinear partial differential equations are solvable. The control law can be easily constructed and the simulations show the feasibility and effectiveness of the controller.     

Predictor–observer-based control of systems with multiple input/output delays

This paper deals with the control of single-input–single-output linear time-delayed systems, when there are different delays in the output/input transfer function. The process can be disturbed and unstable. A new control structure is proposed, solving the problem in several steps. First, by using a stable predictor/observer the plant is stabilized, regardless the delays. On the stable plant, the multidelay plant model is considered as a single delay plant with additional disturbances. The problem of disturbance rejection is solved by using a disturbance observer approach. Finally, output tracking is achieved by a two degrees of freedom controller.     

不确定Euler-Bernoulli梁方程的边界输出跟踪

本文讨论边界带有控制输入非同位的内部不确定和外部扰动的Euler-Bernoulli梁方程输出跟踪问题. 为处理边界干扰, 文章首先设计了一个新的总扰动估计器, 在线估计未知扰动. 其次基于估计出来的总扰动, 设计一个伺服系统跟踪参考信号. 最后根据自抗扰方法获得控制输出跟踪的反馈控制. 闭环系统被证明是适定和有界的, 且受控系统的输出指数跟踪参考信号.     

Nonlinear Adaptive Tracking Of Surface Vessels With Exogenous Disturbances

Significant interaction disturbances in surface vessel maneuvering and position tracking often require high precision controllers. In this paper we develop a coupled nonlinear two‐vessel tracking model for addressing the problem of underway replenishment. Next, using this model we develop an inverse optimal adaptive controller that guarantees disturbance rejection to exogenous disturbances while maintaining a desired separation between the two vessels.     

Static output feedback control design for linear MIMO systems with actuator dynamics governed by diffusion PDEs

This paper deals with the problem of static output feedback (SOF) control design for a class of diffusion partial differential equation (PDE) and ordinary differential equation (ODE) cascades, where the ODE model is used to describe the dynamics of the multi-input and multi-output (MIMO) plant and the diffusion PDE model is employed to represent the dynamics of actuators. The objective of this paper is to develop a simple as well as effective SOF controller via the Lyapunov's direct method such that the resulting closed-loop system is globally exponentially stable. By constructing a quadratic Lyapunov function, the sufficient condition on the globally exponential stability of the closed-loop cascaded system is presented in terms of linear matrix inequality (LMI). Then, an LMI-based design method of the SOF controller is developed on the basis of the obtained stability analysis result. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed design method.     

Moment stability analysis of linear stochastic human controller model in visuomotor tracking task

We investigate the stability limits of linear stochastic human controller model. In our previous study, we had proposed a model by which the probability distributions of human visuomotor tracking data can be accurately reproduced. In this study, we conduct a stochastic analysis on our model by deriving a system of moment differential equations with respect to random state variables of this model. We evaluate the stability limits of our model by detecting zero-eigenvalue conditions of the Jacobian matrix of the moment differential equations. The resulting stability limits make it possible to characterize the human parameter values that were experimentally identified from the human participants in our previous study; this shows that during the visuomotor tracking experiments, the human participants generated huge fluctuations far from the stability limits while applying almost neutrally stable proportional gain.     

Active Vibration Control for a Flexible‐Link Manipulator with Input Constraint Based on a Disturbance Observer

This paper mainly focuses on designing an active vibration control for a flexible‐link manipulator in the presence of input constraint and unknown spatially infinite dimensional disturbances. The manipulator we studied can be taken as an Euler–Bernoulli beam, the dynamic model of which has the form of partial differential equations. As the existence of spatially infinite dimensional disturbances on the beam, we first design a disturbance observer to estimate infinite dimensional disturbances. The proposed disturbance observer is guaranteed exponentially stable. Then, taking input saturation into account, a novel disturbance‐observer‐based controller is developed to regulate the joint angular position and rapidly suppress vibrations on the beam, which is the main contribution of this study. The closed‐loop system is validated asymptotically stable by theoretical analysis. The effectiveness of the proposed scheme is demonstrated by numerical simulations.     

基于弹性能量函数的非线性不确定系统控制方法

针对非线性不确定系统的控制问题,提出一种基于弹性能量函数的扰动观测方法和弹性跟踪控制方法.该方法以弹性能量函数为核心,将其分别应用于扰动观测器、虚拟跟踪指令以及弹性跟踪控制器的设计.该控制方法的突出优势是只根据误差来消除误差,不涉及误差的微分运算,控制器增益参数完全根据积分步长来整定.理论研究表明,所提出的弹性跟踪控制方法不仅可从理论上保证各级子控制器的稳定性,有效解决高阶SISO非线性不确定系统的控制问题,而且可有效避免反步控制方法出现的微分爆炸问题.此外,每个子控制器只有一个由积分步长即可整定的增益参数,因而控制器结构简单、计算量较小.仿真结果表明:所提出的控制方法不仅具有快的响应速度、高的控制精度以及强的抗扰动能力,而且不依赖于被控对象模型,在非线性不确定系统控制领域具有广泛的应用前景.     

Prediction‐based Adaptive Robust Tracking Control of an Uncertain First‐Order Time‐Delay System

This paper considers the tracking problem of a delayed uncertain first‐order system which is simultaneously subject to (possibly large) known input delay, unknown but bounded time‐varying disturbance, and unknown plant parameter. The proposed predictor adaptive robust controller (PARC) involves prediction‐based projection type adaptation laws with model compensation and prediction‐based continuous robust feedback such that the closed loop system has global exponential convergence with an ultimate bound proportional to delay, disturbance bound, and switching gain. Further, if there are only delay and parameter uncertainties after some finite time, then semi‐global asymptotic tracking is guaranteed. The proposed design is shown to have significant closed loop performance improvement over the baseline controller.     

四旋翼无人机鲁棒自适应姿态控制

 四旋翼无人机的姿态控制是自主飞行控制的核心,针对四旋翼姿态易受外界环境干扰和内部参数摄动等不确定性影响的问题,设计了一种鲁棒自适应反步控制器,以提高四旋翼的鲁棒性。建立了四旋翼完整的姿态运动模型,并将其转化为含有广义不确定性的多输入多输出非线性系统。根据该系统满足严格反馈的结构特点,设计了反步控制器; 针对系统中存在的外部干扰和内部参数摄动等不确定性,引入了一类鲁棒自适应函数来抵消该不确定性对系统的影响; 采用非线性跟踪微分器估计虚拟控制量的微分信号,减小了反步控制器设计中普遍存在的“计算膨胀”问题; 通过构造Lyapunov 函数证明闭环系统是稳定且指数收敛的。仿真结果表明,所设计控制器具有良好的控制效果和鲁棒性。     

具有边界扰动的不确定Euler-Bernoulli梁方程输出反馈控制

针对带有边界扰动、内部不确定扰动和外部扰动的Euler-Bernoulli梁方程,为克服传统扰动观测器引入的高增益及未知扰动导数难以准确求解问题,本文将主动干扰抑制控制(ADRC)技术应用到Euler-Bernoulli梁方程这个偏微分方程(PDE)系统上,提出并设计了一种新的在线扰动观测器,可实时估计扰动值.依据估计扰动值,设计了一个边界输出反馈控制器.仿真结果表明,本文所提出的方法可很好地实现对内部不确定扰动和外部扰动的估计,配合输出反馈控制器,可对边界扰动进行有效抑制,进而实现系统的指数稳定.     

Finite dimensional disturbance observer based control for nonlinear parabolic PDE systems via output feedback

This paper considers the problem of finite dimensional disturbance observer based control (DOBC) via output feedback for a class of nonlinear parabolic partial differential equation (PDE) systems. The external disturbance is generated by an exosystem modeled by ordinary differential equations (ODEs), which enters into the PDE system through the control channel. Motivated by the fact that the dominant dynamic behavior of parabolic PDE systems can be characterized by a finite number of degrees of freedom, the modal decomposition technique is initially applied to the PDE system to derive a slow subsystem of finite dimensional ODEs. Subsequently, based on the slow subsystem and the exosystem, a disturbance observer (DO) and a slow mode observer (SMO) are constructed to estimate the disturbance and the slow modes. Moreover, an observation spillover observer (OSO) is also constructed to cancel approximately the effect of the observation spillover. Then, a finite dimensional DOBC design via output feedback is developed to estimate and compensate the disturbance, such that the closed-loop PDE system is exponentially stable in the presence of the disturbance. The condition for the existence of the proposed controller is given in terms of bilinear matrix inequality. Two algorithms based on the linear matrix inequality (LMI) technique are provided for solving control and observer gain matrices of the proposed controller. Finally, the developed design method is applied to the control of a one-dimensional diffusion-reaction process to illustrate its effectiveness.     

Boundary control of a parallel-flow heat exchanger by input–output linearization

A design of the control of the internal fluid temperature at the outlet of a parallel-flow heat exchanger by manipulating the inlet external fluid temperature is proposed. The dynamic model of the heat exchanger is given by two partial differential equations that are used without spatial discretization to design the control law. Based on nonlinear control, a state-feedback law that ensures a desired performance of a measured output defined as the spatial weighted average temperature of the internal fluid is derived. Then, in order to control the outlet internal fluid temperature, a control strategy is proposed where an external controller is introduced to provide the set point of the considered measured output by taking as input the error between the outlet internal fluid temperature and its desired set point. As the designed control law is a state feedback of distributed nature, for practical application, a Kalman filter is used to reconstruct the entire state of the system from the measurements of the outlet fluids temperatures. The closed-loop system is shown to be exponentially stable. The validity of the proposed control design is examined in simulation by considering the tracking and perturbation rejection problems.     

Iterative learning of model reference adaptive controller for uncertain nonlinear systems with only output measurement

In this paper, a model reference adaptive control strategy is used to design an iterative learning controller for a class of repeatable nonlinear systems with uncertain parameters, high relative degree, initial output resetting error, input disturbance and output noise. The class of nonlinear systems should satisfy some differential geometric conditions such that the plant can be transformed via a state transformation into an output feedback canonical form. A suitable error model is derived based on signals filtered from plant input and output. The learning controller compensates for the unknown parameters, uncertainties and nonlinearity via projection type adaptation laws which update control parameters along the iteration domain. It is shown that the internal signals remain bounded for all iterations. The output tracking error will converge to a profile which can be tuned by design parameters and the learning speed is improved if the learning gain is large.     

Robust integral control for a class of nonlinear systems with unknown control coefficients

The robust integral control problem is studied for a class of nonlinear systems with input-to-state stable (ISS)unmodeled dynamics in this paper.It does not require a priori knowledge of the control coefficients.Combining the Nussbaum-type gain technique and the backstepping design,we propose a state feedback controller,which could achieve the global asymptotic tracking for any constant reference signal,irrespective of the unmeasured dynamic disturbance.It is shown that the proposed methodology further extends the existing robust nonlinear integral control results.Simulation results verify the correctness of the theoretical analysis.     

Variable-Gain Controllers for Nonlinear Systems Using the T–S Fuzzy Model

This correspondence proposes two novel control schemes with variable state-feedback gain to stabilize a Takagi-Sugeno (T-S) fuzzy system. The T-S fuzzy model is expressed as a linear plant with nonlinear disturbance terms in both schemes. In controller I, the T-S fuzzy model is expressed as a linear plant around a nominal plant arbitrarily selected from the set of linear subsystems that the T-S fuzzy model consists of. The variable gain then becomes a function of a gain parameter that is computed to neutralize the effect of disturbance term, which is, in essence, the deviation of the actual system dynamics from the nominal plant as the system traverses a specific trajectory. This controller is shown to stabilize the T-S fuzzy model. In controller II, individual linear subsystems are locally stabilized. Fuzzy blending of individual control actions is shown to make the T-S fuzzy system Lyapunov stable. Although applicability of both control schemes depends on the norm bound of unmatched state disturbance, this constraint is relaxed further in controller II. The efficacy of controllers I and II has been tested on two nonlinear systems