The variable structure controller design for a class of nonlinear uncertain systems based on robust observer

The variable structure controller is designed for a class of nonlinear uncertain time-delay system by using robust observer, and incorporating H-infinity control technique, the controller can guarantee the H-infinity performance of sliding mode dynamics and satisfy the reaching condition, which also does not require uncertainties to satisfy matching condition and linear boundary condition. The simulation example is given to illustrate the method.     

An optimal robust design method for fractional-order reset controller

In this paper, a novel design method for the reset controller structure (i.e., fractional-order proportional and integral plus Clegg integrator (PI ${}^{\alpha }$ + CI ${}^{\alpha }$)), is proposed for a second-order plus time delay plant. To this end, the designer can get an optimal fractional reset controller that gives the control system more phase margin over the base linear PI controller and robust to loop gain variation. The describing function method is used to investigate the capability of phase lead and the frequency domain properties of PI ${}^{\alpha }$ + CI ${}^{\alpha }$. The gain crossover frequency and phase margin specifications ensure the stability of the control system, and the flat phase constraint makes the control system robust to loop gain variations. Meanwhile, the integral of time and absolute error (ITAE) value is applied to achieve the optimal dynamic performance as the cost function. PI ${}^{\alpha }$ + CI ${}^{\alpha }$ is compared with its integer-order counterpart (i.e., proportional and integral plus Clegg integrator (PI + CI) controller) and their base controllers (i.e., integer-order PI and fractional-order PI controllers) in terms of the step response and robustness to loop gain variations. The simulation results illustrate that the PI ${}^{\alpha }$ + CI ${}^{\alpha }$ control system obtains lower overshoot and oscillation and better robustness to loop gain variations than others. The experiments are performed on the speed control of an air bearing stage. Experimental results show that the designed PI ${}^{\alpha }$ + CI ${}^{\alpha }$ control system behaves better than others. The proposed PI ${}^{\alpha }$ + CI ${}^{\alpha }$ design method can be applied to other general control plants easily.     

A multirule-base controller using the robust property of a fuzzycontroller and its design method

This paper suggests a new fuzzy adaptive controller, which is able to solve the problems of classical adaptive controllers and conventional fuzzy adaptive controllers. It explains the architecture of a fuzzy adaptive controller using the robust property of a fuzzy controller. The basic idea of new adaptive control scheme is that an adaptive controller can be constructed with parallel combination of robust controllers. This new adaptive controller uses a multirule-base architecture which has several independent fuzzy controllers in parallel, each with different robust stability area. Out of several independent fuzzy controllers, the most suited one is selected by a system identifier which observes variations in the controlled system parameter. Here, we propose a design procedure which can be carried out mathematically and systematically from the model of a controlled system; related mathematical theorems and their proofs are also given. The performance of the proposed adaptive control algorithm is analyzed through a design example and a DC motor control simulation     

A systematic approach for robust repetitive controller design

In this paper, a methodology for the synthesis of repetitive controllers to ensure periodic reference tracking and harmonic disturbance rejection is cast in a robust control framework. Specifically, the Lyapunov–Krasovskii theory is applied to derive LMI-based conditions for designing a state feedback control law with guaranteed stability and performance properties for system parameter variations. Practical experiments in commercial uninterruptible power supplies – UPS are considered to illustrate and discuss some practical implementation aspects of the proposed method.     

Adaptive observer design for robust fault estimation

In this article, fault diagnosis for a class of linear systems based on adaptive observer is investigated. Linear systems without model uncertainty are first considered, and two adaptive observers are designed for fault identification. The first one uses optimal design for minimizing the estimation error. The second one can achieve asymptotic fault estimation. The general situation where the system is subjected to either model errors or external disturbance is then discussed. Robust adaptive control techniques are applied to guarantee the convergence to a bounded set. Simulation of sensor fault diagnosis for an induction motor is presented to verify the effectiveness of the proposed method.     

PID controller design for robust performance

This note is devoted to the problem of synthesizing proportional-integral-derivative (PID) controllers for robust performance for a given single-input-single-output plant in the presence of uncertainty. First, the problem of robust performance design is converted into simultaneous stabilization of a complex polynomial family. An extension of the results on PID stabilization is then used to devise a linear programming design procedure for determining all admissible PID gain settings. The most important feature of the proposed approach is that it computationally characterizes the entire set of the admissible PID gain values for an arbitrary plant.     

一种鲁棒的自适应带宽跟踪方法

在自适应带宽均值移动算法的基础上, 引入粒子滤波, 提出一种新的目标跟踪方法. 该方法通过更新带宽矩阵以适应目标尺度的变化; 采用加权和方法融合定位检测结果, 使跟踪不易陷入局部最优状态; 对粒子进行收敛采样, 维持粒子多样性, 减小累积误差; 提出一种目标扩展搜索策略, 用于目标丢失后重新搜索跟踪目标. 实验结果表明, 所提出的跟踪方法在复杂场景中表现出了较好的鲁棒性, 且跟踪轨迹平滑.

     

直线伺服系统非线性自适应鲁棒控制器的优化设计

对永磁直线电动机伺服系统提出了非线性自适应鲁棒控制器的优化设计方法.在系统非线性数学模型的基础上,建立了误差系统的动态模型.将跟踪和干扰抑制归结为非线性自适应鲁棒控制器的设计问题,通过构造存储函数得到自适应鲁棒控制器的定理,以及电阻和电感的辨识算法.证明了定理给出的控制器能满足干扰抑制和系统渐近稳定,并用遗传算法对控制器的参数进行优化.仿真结果验证了该方法是有效的.     

Modified observer backstepping controller for a dynamic positioning system

A procedure for attenuating the control law of a vessel dynamic positioning system, based on the observer backstepping methodology, is proposed. The motivation is the appearance of an undesirable on–off behavior on the signal sent to the actuators when their saturation is considered and the control law is dependent on estimated state variables. Two gain matrices associated with the error variables are introduced to achieve the desired attenuation. Stability is proven through Lyapunov stability analysis. Numerical simulations confirm the effectiveness of the proposed controller to render the control law compatible with the limitations of the actuators.     

Sequential LMI approach for the design of a BMI‐based robust observer state feedback controller with nonlinear uncertainties

This paper aims at developing a robust observer–based estimated state feedback control design method for an uncertain dynamical system that can be represented as a linear time‐invariant system connected with an integral quadratic constraint–type nonlinear uncertainty. Traditionally, in existing design methodologies, a convex semidefinite constraint is obtained at the cost of conservatism and unrealistic assumptions. This paper avoids such assumptions and formulates, the design of the robust observer state feedback controller as the feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP‐hard problem in general. The applicability of a linearization method, such as the variable change method and the congruence transformation, depends on the specific structure of the problem at hand and cannot be generalized. This paper transforms the feasibility analysis of the BMI constraint into an eigenvalue problem and applies the convex‐concave–based sequential linear matrix inequality optimization method to search for a feasible solution. Furthermore, an augmentation of the sequential linear matrix inequality algorithm to improve its numerical stability is presented. In the application part, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real‐world estimated state feedback control design problem and the necessity of the augmentation for numerical stability.     

Energy-based robust controller design for flexible spacecraft

This paper presents a class of non-model2based position controllers for a kind of flexible spacecraft. With the controllers, one can achieve not only the closed-loop stability of the original distributed parameter system, but also the asymptotic stability of the truncated system, which is obtained through representing the deflection of the appendage by an arbitrary finite number of flexible modes. The system dynamics are not explicitly involved in the controller design and stability proof. Instead, only a very basic system energy rehtionship of the flexible spacecraft is utilized. The controllers possess several remarkable advantages over the traditional model-based ones. Numerical simulations are carried out on a kind of spacecraft with one flexible appendage and satisfactory results are obtained.     

高超声速飞行器非线性鲁棒控制律设计

高超声速飞行器具有模型非线性程度高、耦合程度强、参数不确定性大、抗干扰能力弱等特点,其自主控制具有较大的挑战.论文提出了一种基于鲁棒补偿技术和反馈线性化方法的非线性鲁棒控制方法.文中首先采用反馈线性化的方法对纵向模型进行输入输出线性化,实现速度和高度通道的解耦和非线性模型的线性化.针对得到的线性模型,设计包括标称控制器和鲁棒补偿器的线性控制器.基于极点配置原理,设计标称控制器使标称线性系统具有期望的输入输出特性,利用鲁棒补偿器来抑制参数不确定性和外界扰动对于闭环控制系统的影响.基于小增益定理,证明了闭环控制系统的鲁棒稳定性和鲁棒跟踪性能.相比于非线性回路成形控制方法,仿真结果表明了所设计非线性鲁棒控制算法的有效性和优越性.     

直接转矩控制系统的稳定性问题和鲁棒控制器设计

直接转矩控制(DTC)系统的设计不依赖于感应电机的转子参数,但它的低速性能不好.研究发现,即使定子电阻测量得足够准确,根据定子磁链的电压电流模型设计的经典DTC系统的低速性能仍得不到改善.理论分析说明了这些问题存在的必然性,指出了DTC系统在转矩控制和稳定性之间存在的矛盾,给出了一种鲁棒控制器的设计方案.该方案同时使用了定子电阻和定子磁链的电流模型,当定子电阻和磁链模型出现误差时,表现出了好的鲁棒性.实验结果验证了系统的性能.     

Time forward observer based adaptive controller for a teleoperation system

This paper presents a design of a teleoperation system using time forward observer-based adaptive controller. The controller is robust to the time-variant delays and the environmental uncertainties while assuring the stability and the transparent performance. A novel theoretical framework and algorithms for this teleoperation system have been built up with neural network-based multiple model control and time forward state observer. Conditions for stability and transparency performance are also investigated.     

硬盘电机伺服系统的低阶鲁棒控制器设计

针对模型不确定情况下硬盘电机伺服系统的精确控制问题,给出了硬盘电机伺服系统的控制关系模型.采用优化H∞控制技术设计了简单高效的鲁棒控制器,并通过控制关系模型估算和闭环控制器衰减使控制器降阶,可以降低控制器设计的复杂度,有效改善系统频率响应,满足设计带宽要求.仿真实验结果表明,系统能够提供的最大带宽和设计带宽相一致,说明了低阶鲁棒控制器的有效性.     

A nonlinear robust PI controller for an uncertain system

This paper presents a smooth control strategy for the regulation problem of an uncertain system, which assures uniform ultimate boundedness of the closed-loop system inside of the zero-state neighbourhood. This neighbourhood can be made arbitrarily small. To this end, a class of nonlinear proportional integral controllers or PI controllers was designed. The behaviour of this controller emulates very close a sliding mode controller. To accomplish this behaviour saturation functions were combined with traditional PI controller. The controller did not need a high-gain controller or a sliding mode controller to accomplish robustness against unmodelled persistent perturbations. The obtained closed-solution has a finite time of convergence in a small vicinity. The corresponding stability convergence analysis was done applying the traditional Lyapunov method. Numerical simulations were carried out to assess the effectiveness of the obtained controller.     

Interpolating sliding mode observer for a ball and beam system

ABSTRACT

A principle of interpolating sliding mode observer is introduced in this paper. The observer incorporates multiple linear observers through interpolation of multiple estimates, which is treated as a type of adaptation. The principle is then applied to the ball and beam system for observation of the slope of the beam from the measurement of the ball position. The linearised model of the ball and beam system using multiple linearisation points is developed. The observer dynamics implemented in Matlab/Simulink Real Time Workshop environment. Experiments conducted on the ball and beam experimental setup demonstrate excellent performance of the designed novel interpolating (adaptive) observer.     

A robust controller for trajectory tracking of a DC motor pendulum system

This work presents a solution to the output feedback trajectory tracking problem for an uncertain DC motor pendulum system under the effect of an unknown bounded disturbance. The proposed algorithm uses a Proportional Derivative (PD) controller plus a novel on-line estimator of the unknown disturbance. The disturbance estimator is obtained by coupling a standard second-order Luenberger observer with a third-order sliding modes differentiator. The Luenberger observer provides estimates of the motor angular position and velocity. Moreover, an ideal disturbance estimator in terms of the Luenberger observer error and its first and second time derivatives is obtained from the observer error formulae; these time derivatives are not available from measurements. Subsequently, the sliding modes third-order differentiator allows obtaining estimates of these time derivatives in finite time. The estimates replace the real values of the first and second time derivatives in the ideal disturbance estimator thus producing a practical disturbance estimator, and also permit obtaining an estimate of the motor angular velocity. A depart from previous approaches is the fact that the disturbance is not directly estimated by the Luenberger observer or the third-order differentiator. Numerical simulations and real-time experiments validate the effectiveness of the proposed approach.     

降低参数灵敏度的磁浮列车鲁棒悬浮控制器设计

磁浮列车的悬浮静态工作点与承载重量有关,因此对悬浮控制器的设计提出了更高的要求.以八达岭磁浮列车旅游线用的CMS-3型磁浮列车为研究对象,在分析磁浮列车悬浮控制系统的数学模型基础上,应用降低参数灵敏度的鲁棒控制器设计法对悬浮控制器进行设计,使控制器对列车质量变化的参数灵敏度明显降低.