一类具有饱和因子的奇异时滞系统的鲁棒保性能控制

研究了具有饱和因子的非线性奇异时滞系统的鲁棒保性能控制问题.目的是设计一个鲁棒控制器和保成本控制器,通过线性矩阵不等式方法(LMI)得出了鲁棒控制器和保性能控制器存在的充分条件.当这些LMI方法是可解时,分别给出了鲁棒控制器和保性能控制器的解析表达式.     

Composite nonlinear feedback based discrete integral sliding mode controller for uncertain systems

In this paper, a discrete integral sliding mode (ISM) controller based on composite nonlinear feedback (CNF) method is proposed. The aim of the controller is to improve the transient performance of uncertain systems. The CNF based discrete ISM controller consists of a linear and a nonlinear term. The linear control law is used to decrease the damping ratio of the closed-loop system for yielding a quick transient response. The nonlinear feedback control law is used to increase the damping ratio with an aim to reduce the overshoot of the closed-loop system as it approaches the desired reference position. It is observed that the discrete CNF-ISM controller produces superior transient performance as compared to the discrete ISM controller. The closed-loop control system remains stable during the sliding condition. Simulation results demonstrate the effectiveness of the proposed controller.     

一类具有闭环极点约束的不确定线性系统的保性能控制

主要研究了闭环系统的极点约束在一个给定圆盘中的保性能控制问题,基于线性矩阵不等式处理方法给出了状态反馈控制器存在的充要条件,并利用线性矩阵不等式的解给出了保性能控制器的设计方法,得到一个状态反馈控制器,使得对所有允许的不确定性闭环系统稳定,并且闭环性能指标值不超过某个确定的上界.最后以数值例子验证了结果的正确性.     

Fuzzy guaranteed cost controller for trajectory tracking in nonlinear systems

In this paper, we propose a fuzzy logic based guaranteed cost controller for trajectory tracking in nonlinear systems. Takagi–Sugeno (T–S) fuzzy model is used to represent the dynamics of a nonlinear system and the controller design is carried out using this fuzzy model. State feedback law is used for building the fuzzy controller whose performance is evaluated using a quadratic cost function. For designing the fuzzy logic based controller which satisfies guaranteed performance, linear matrix inequality (LMI) approach is used. Sufficient conditions are derived in terms of matrix inequalities for minimizing the performance function of the controller. The performance function minimization problem with polynomial matrix inequalities is then transformed into a problem of minimizing a convex performance function involving standard LMIs. This minimization problem can be solved easily and efficiently using the LMI optimization techniques. Our controller design method also ensures that the closed-loop system is asymptotically stable. Simulation study is carried out on a two-link robotic manipulator tracking a reference trajectory. From the results of the simulation study, it is observed that our proposed controller tracks the reference trajectory closely while maintaining a guaranteed minimum cost.     

不确定线性系统的最优保性能可靠控制

针对一类不确定线性系统,采用连续增益故障模型提出了考虑执行器故障的保性能可靠控制问题.通过对具有执行器增益故障的系统分析,利用线性矩阵不等式(LMI)分别给出了保性能标准控制、最优保性能标准控制、保性能可靠控制、最优保性能可靠控制存在的充分条件.根据凸优化理论,最优保性能标准控制和最优保性能可靠控制的设计方法转化为一个线性凸优化算法.仿真数例验证了文中所提出方法的可行性.在相同形式的故障发生时,比较最优保性能标准控制与最优保性能可靠控制,进一步说明了最优保性能可靠控制的必要性.     

Dual-Sampling-Rate Moving-Horizon Control of a Class of Linear Systems with Input Saturation and Plant Uncertainty

Moving-horizon control is a type of sampled-data feedback control in which the control over each sampling interval is determined by the solution of an open-loop optimal control problem. We develop a dual-sampling-rate moving-horizon control scheme for a class of linear, continuous-time plants with strict input saturation constraints in the presence of plant uncertainty and input disturbances. Our control scheme has two components: a slow-sampling moving-horizon controller for a nominal plant and a fast-sampling state-feedback controller whose function is to force the actual plant to emulate the nominal plant. The design of the moving-horizon controller takes into account the nonnegligible computation time required to compute the optimal control trajectory.We prove the local stability of the resulting feedback system and illustrate its performance with simulations. In these simulations, our dual-sampling-rate controller exhibits performance that is considerably superior to its single-sampling-rate moving-horizon controller counterpart.     

A robust neurocontroller incorporating a priori knowledge of plant dynamics

This paper presents a nonlinear controller design method that integrates linear optimal control techniques and nonlinear neural networks. The multilayered neural networks (MNN's) are incorporated into a model-based linear optimal controller (LOR) to add nonlinear effects on the LOR. The proposed controller can tolerate a wider range of uncertainties than the LOR alone, because the MNN can compensate nonlinear system uncertainties that are not considered in the LOR design. The control performance is improved by using a priori knowledge of the plant dynamics as the system equation and the corresponding LOR. Using the similar technique, a nonlinear servo controller is designed by combining the MNN-based controller and the linear optimal servo controller. Computer simulations are performed to show the applicability and the limitation of the new nonlinear controllers.     

A general result in stochastic optimal control of nonlinear discrete-time systems with quadratic performance criteria

It is known that the optimal controller for a linear dynamic system disturbed by additive, independently distributed in time, not necessarily Gaussian, noise is a linear function of the state variables if the performance criterion is the expected value of a quadratic form. This result is known to hold also when the noise is Gaussian and is multiplied by a linear function of the state and/or control variables.In this paper it is proved that the optimal controller for a discrete-time linear dynamic system with quadratic performance criterion is a linear function of the state variables when the additive random vector is a nonlinear function of the state and/or control variables and not necessarily Gaussian noise which is independently distributed in time, provided only that the mean value of the random vector is zero (there is no loss of generality in assuming this) and the covariance matrix of the random vector is a quadratic function of the state and/or control variables. The above-mentioned known results emerge as special cases and certain nonlinear other special cases are exhibited.     

GUARANTEED COST CONTROL OF CONTINUOUS-TIME UNCERTAIN SINGULAR SYSTEM WITH BOTH STATE AND INPUT DELAYS

The guaranteed cost control problem for a continuous-time uncertain singular system with state and control delays, and a given quadratic cost function is studied in this paper. Sufficient conditions for the existence of the guaranteed cost controller are derived based on the linear inequality (LMI) approach. A parameterized characterization of the guaranteed cost laws is given in terms of the feasible solutions to a certain LMI, and the cost function of guaranteed cost controller exists an upper bound.     

Delay-dependent nonfragile guaranteed cost control for nonlinear time-delay systems

This paper concerns the nonfragile guaranteed cost control problem for a class of nonlinear dynamic systems with multiple time delays and controller gain perturbations. Guaranteed cost control law is designed under two classes of perturbations, namely, additive form and multiplicative form. The problem is to design a memoryless state feedback control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Based on the linear matrix inequality (LMI) approach, some delay-dependent conditions for the existence of such controller are derived. A numerical example is given to illustrate the proposed method.     

Improving the performance of linear controllers through nonlinear perturbations: Applications to one-dimensional systems

Linear control techniques have been widely used for controlling both linear and nonlinear systems. In this paper we show the design of a kind of nonlinear controllers starting from the standard procedure for designing linear controllers by pole placement. After the linear controller is designed, we add a nonlinear term with the aim to improve the system performance together with the significant decrease of the control effort. The methodology is developed through an example corresponding to a one-dimensional system. The stability and control effort are proved in analytical way and the performance of the system is tested numerically and analytically.     

Lead with closed-loop system compensation of a radically rotating elastic rod attached to a rigid body part I: A unified approach to the design of Llnear control system

Due to difficulties in modeling and poor knowledge of parameters, the behavior of flexible structures is subject to significant uncertainty. Hence it is essential that the control system provide an absolutely stable property in the presence of large variations. Over the years, many control laws—proportion and derivative (PD) control, nonlinear, linear-quadratic, adaptive, and linear quadratic Gaussian (LQG)—have been synthesized for flexible structures. The most commonly applied are the LQG controllers. In spite of its attractive qualities, the LQG controller is sensitive to parameter variations, and therefore its performance will deteriorate when the payload or typical parameters of the system vary with time. At the same time, the LQG controller does not guarantee general stability margins, and this is, perhaps, its main drawback. On the other hand, the PD is one kind of controller that ensures system stability to parameter variations within a certain bound. But a problem with the PD controller is evident; when high-frequency noise is present in the system, this noise will be amplified by the PD controller, which is generally unacceptable. In this paper, instead of using a PD controller, a passive lead compensator is employed, so that

• 1.(1) no additional power supplies are required and
• 2.(2) noise due to differentiation is reduced.

This lead compensator, together with a composite control strategy designed by the most popularly used sensors, potentiometer and tachometer, for the corresponding closed-loop system, has been shown with very good agreement in terms of system performance requirement. For the design of control system, it is practical to first design the controller based on the linear system model by neglecting the nonlinearities of the system. In Part I, the lead compensator, together with complementary control strategy and computer simulation modeling for a rotating flexible structure, with particular application to elastic rod system, is presented for the linear control system. Then the designed controller is applied to the nonlinear system model for evaluation and redesigned by computer simulation. This will be presented in Part II.     

On Dynamic Output Feedback Guaranteed Cost Control of Uncertain Discrete-Delay Systems: LMI Optimization Approach

In this paper, we consider a design problem of dynamic output feedback controller for guaranteed cost stabilization of discrete-delay systems with norm-bounded time-varying parameter uncertainties. A linear-quadratic cost function is considered as a performance measure for the closed-loop system. Based on the Lyapunov second method, several stability criteria for the existence of the controller are derived in terms of linear matrix inequalities (LMIs). The solutions of the LMIs can be obtained easily using existing efficient convex optimization techniques. A numerical example is given to illustrate the proposed method.     

Multi-model predictive control of Hammerstein-Wiener systems based on balanced multi-model partition

ABSTRACT

Model analysis of Hammerstein-Wiener systems has been made, and it is found that the included angle is applicable to such systems to measure the non-linearity. Then, a dichotomy gridding algorithm is proposed based on the included angle. Supporting by the gridding algorithm, a balanced multi-model partition method is put forward to partition a Hammerstein-Wiener system into a set of local linear models. For each linear model, a linear model predictive controller (MPC) is designed. After that, a multi-MPC is composed of the linear MPCs via soft switching. Thus, a complex non-linear control problem is transformed into a set of linear control problems, which simplifies the original control problem and improves the control performance. Two non-linear systems are built into Hammerstein-Wiener models and investigated using the proposed methods. Simulations demonstrate that the proposed gridding and partition methods are effective, and the resulted multi-MPC controller has satisfactory performance in both set-point tracking and disturbance rejection control.     

Output Feedback Guaranteed Cost Control for Uncertain Discrete-Time Systems Using Linear Matrix Inequalities

This paper considers the output feedback guaranteed cost controller design problem for uncertain discrete-time systems. The uncertainty is assumed to be of linear fractional form, unstructured, and is allowed to be time-varying. It is proved that the existence of a guaranteed cost controller is equivalent to the feasibility of a certain linear matrix inequality (LMI), and that a full-order output feedback controller can be constructed in terms of the feasible solution to the LMI. Furthermore, a convex optimization problem is introduced for the selection of a suitable controller minimizing a specified cost bound.     

广义连续系统极小极大控制反问题初探

将极小极大控制的反问题推广到广义系统.针对给定的性能指标,通过受限等价变换,得到判别广义连续系统控制器是极小极大控制器的充要条件及其等价的频率条件.最后针对广义系统H∞次优控制的反问题进行了讨论.     

Nonlinear sliding surface based second order sliding mode controller for uncertain linear systems

A second order sliding mode (SOSM) controller using nonlinear sliding surface is proposed in this paper. The aim of the proposed controller is to guarantee stability as well as enhance the transient performance of uncertain linear systems with parametric uncertainty. The nonlinear sliding surface consists of a linear term and a nonlinear term. The linear term comprises a gain matrix which has a very low value of damping ratio and thereby facilitates fast response. The nonlinear term is introduced to accommodate a variable damping ratio to reduce overshoot and settling time of the closed loop system as the output reaches nearer the desired reference position. A major gain of the proposed SOSM controller is the elimination of chattering in the control input. The proposed nonlinear sliding surface based SOSM controller achieves fast rise, low overshoot and low settling time. Simulation results demonstrate the effectiveness of the proposed SOSM controller.     

AQM scheme design for TCP network via Takagi‐Sugeno fuzzy method

This paper proposes a novel T‐S fuzzy control method instead of the traditional linear system control method to improve the TCP network performance. Thus a TCP network can be modeled as a T‐S fuzzy system, and by use of linear matrix inequality method and cone complementarity linearization algorithm, a fuzzy state feedback controller is provided while considering the problem of the asynchronous membership grades between the controller and the plant. Simulation results are presented to show that the proposed control approach can guarantee the asymptotical stability of the studied system and the desired queue size. © 2016 Wiley Periodicals, Inc. Complexity 21: 606–612, 2016     

Iterative identification and control design using finite-signal-to-noise models

In this paper, a model is said to be validated for control design if using the model-based controller, the closed loop performance of the real plant satisfies a specified performance bound. To improve the model for control design, only closed loop response data is available to deduce a new model of the plant. Hence the procedure described herein involves three steps in each iteration: (i) closed loop identification; (ii) plant model extraction from the closed loop model; (iii) controller design. Thus our criteria for model validation involve both the control design procedure by which the closed loop system performance is evaluated, and the identification procedure by which a new model of the plant is deduced from the closed loop response data. This paper proposes new methods for both parts, and also proposes an iterative algorithm to connect the two parts. To facilitate both the identification and control tasks, the new finite-signal-to-noise (FSN) model of linear systems is utilized. The FSN model allows errors in variables whose noise covariances are proportional to signal covariances. Allowing the signal to noise ratios to be bounded but uncertain, a control theory to guarantee a variance upper bound is developed for the discrete version of this new FSN model. The identification of the closed loop system is accomplished by a new type of q-Markov Cover, adjusted to accommodate the assumed FSN structure of the model. The model of the plant is extracted from the closed loop identification model. This model is then used for control design and the process is repeated until the closed loop performance validates the model. If the iterations produce no such a controller, we say that this specific procedure cannot produce a model valid for control design and the level of the required performance must be reduced.