Multiple robust H∞ controller design using the nonsmooth optimization method

This paper proposes a systematic technique to design multiple robust H_∞ controllers. The proposed technique achieves a desired robust performance objective, which is impossible to achieve with a single robust controller, by dividing the uncertainty set into several subsets and by designing a robust controller to each subset. To achieve this goal with a small number of divisions of the uncertainty set, an optimization problem is formulated. Since the cost function of this optimization problem is not a smooth function, a numerical nonsmooth optimization algorithm is proposed to solve this problem. This method avoids the use of Lyapunov variables, and therefore it leads to a moderate size optimization problem. A numerical example shows that the proposed multiple robust control method can improve the closed‐loop performance when a single robust controller cannot achieve satisfactory performance. Copyright © 2009 John Wiley & Sons, Ltd.     

A study of robust controller and observer design method for a rolling object and beam system

This paper deals with a robust control problem for a ball and beam system with an uncertainty. At first, we clarify the effect of a measurement error in the beam rotational angle and its differential value. It is expressed as additional terms in the state and input matrix of the state equation, which is called as a structured uncertainty. For this system, a robust tracking controller and a robust state observer are applied. Both components are designed based on a robust control, which is called guaranteed cost control. This is a kind of cost minimization method for designing problem of a linear feedback system. The controller is obtained as the solution of the matrix algebraic Riccati like equation, which is referred to as stochastic algebraic Riccati equation. The nominal system performance is degraded due to the influence of the uncertainty, but it is able to design a system with robustness for disturbance. Next, we consider the design problem of a state observer to estimate all state variables form the output signal easy to measure, like rotation angle of the beam. For the design problem of the state observer, we consider dual problem of the original system. Consequently, our proposed system estimates the whole state vector, and using estimated state values, it controls the ball to the desired position. Both components have robustness for the uncertainty. Numerical result shows the validity of our proposed 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 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.     

飞行器模型簇描述及鲁棒控制器设计

通过分析飞行器运动方程，给出了分段线性化模型簇描述．为了得到一定飞行区域的鲁棒控制器，选取负实极点并采用对角占优势的方法对状态反馈矩阵进行设计．同时，提出了全飞行区域(飞行包线内)的多个子系统划分及鲁棒镇定控制的设计方法．为了抑制飞行器的建模误差，采用了输入补偿方法．与常规鲁棒控制设计方法相比较，该方法可以降低飞行控制器设计的复杂度．飞行控制器设计结果表明，该方法对不确定系统的分析和设计是有效的。     

Stabilisation using a stable controller and robust stability and performance

A class of strictly proper multi-input multi-output (MIMO) causal linear time invariant (LTI) systems with a detectable and stabilisable realisation in a proposed observer-controller scheme, is considered. This class is characterised by the rank of the observability matrix in closed loop. The considered scheme is based on an ?_∞ pre-compensator and on an ?_∞ dual post-compensator stabilising a full actuation full information plant and on pseudo inverses of the input and of the output matrices. The pre-compensator and post-compensator are of reduced complexity and belong to the family of all stabilising controllers. The separation principle is satisfied and necessary and sufficient stability conditions are presented for the overall system getting a stable ?_∞ controller. An algebraic approach and a state space approach are used to find this stability condition. The estimated error is zero in stationary state. Also, the control parameters allow the stationary state error and the complementary sensitivity function in high frequencies to approach zero asymptotically. So, robust stability and performance are achieved. A compromise exists between the stability of the compensators and the robust performance objective. The results are illustrated on a mechanical system.     

Adaptive fuzzy robust tracking controller design via small gain approach and its application

An adaptive fuzzy robust tracking control (AFRTC) algorithm is proposed for a class of nonlinear systems with the uncertain system function and uncertain gain function, which are all the unstructured (or nonrepeatable) state-dependent unknown nonlinear functions arising from modeling errors and external disturbances. The Takagi-Sugeno type fuzzy logic systems are used to approximate unknown uncertain functions and the AFRTC algorithm is designed by use of the input-to-state stability approach and small gain theorem. The algorithm is highlighted by three advantages: 1) the uniform ultimate boundedness of the closed-loop adaptive systems in the presence of nonrepeatable uncertainties can be guaranteed; 2) the possible controller singularity problem in some of the existing adaptive control schemes met with feedback linearization techniques can be removed; and 3) the adaptive mechanism with minimal learning parameterizations can be obtained. The performance and limitations of the proposed method are discussed. The uses of the AFRTC for the tracking control design of a pole-balancing robot system and a ship autopilot system to maintain the ship on a predetermined heading are demonstrated through two numerical examples. Simulation results show the effectiveness of the control scheme.     

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.     

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.     

A robust adaptive performance enhancement controller using setmembership identification

A robust direct adaptive control scheme is proposed to enhance the performance of a fixed nominal controller. The key idea lies in the introduction of a set membership constraint in the estimation process. The set membership constraint results in an adaptive scheme that has a built-in discriminator to discard incoming data that carry little or no information content on the actual plant. The proposed scheme, which uses only informative data to refine the parameter estimates, is more robust than conventional methods that continuously update the parameter estimates     

A self-tuning robust controller

The self-tuning robust controller described in this paper has an error-driven, “robust” structure (Francis and Wonham, J. Appl. Math. Opt., 2, 170–194, 1975; Davison, IEEE Trans. Aut. Control, AC-21, 25–34, 1976) which guarantees asymptotic regulation and tracking in the presence of finite parameter perturbations. The controller utilizes unity feedback and also incorporates an internal model of the external disturbances and set points. The adaptive mechanism tunes the controller parameters such that a quadratic performance index with control weighting is minimized. The adaptive algorithm includes a dead zone and ensures global stability of the system in the presence of bounded noise and disturbances. In its simpler and natural form it can also be formulated to be structurally equivalent to a conventional, discrete PID controller. Experimental evaluation of the proposed controller on a pilot-scale evaporator illustrates its practicality.     

Tuning an adaptive controller using a robust control approach

This article proposes a new technique for the tuning of a discrete adaptive controller that is designed based on Lyapunov stability concepts. The tuning is based on the minimisation of a performance index that can be calculated from a generalised eigenvalue problem (GEVP) using LMI's (Linear Matrix Inequalities). The proposed technique results in an adaptive controller with time-varying tuning gains. The solution is based on an approximation of the optimal dual adaptive control problem. The tuning technique was used to perform on-line control of a first-order system and an isothermal and a non-isothermal CSTR. The results show that the proposed approach provides better performance than an adaptive algorithm with the same structure, but with constant adaptation gains. Also, the proposed algorithm is shown to be superior to an adaptive controller based on a Recursive Least Squares (RLS) estimator during sudden changes in model parameters.     

Mobile robot path tracking using a robust PID controller

This paper presents a simple and effective solution for the path tracking problem of a mobile robot using a PID controller. The proposed method uses a simple linearized model of the mobile robot composed of an integrator and a delay. The synthesis procedure is simple and allows the PID controller to be tuned considering the nominal performance and the robustness as control specifications. Experimental results demonstrate the good performance and robustness of the proposed controller.     

异步电机鲁棒控制器及其Backstepp ing 设计

基于异步电机的精确模型,用Backstepping方法设计控制器,其误差系统在原点全局稳定。然而,由于反馈量的计算受参数不确定性和“可导条件”的影响,使得控制器鲁棒性较差,采用扩张状态观测器来增强鲁棒性,无需电机的精确模型,即可准确地获得反馈量,新控制器结合了Backstepping和扩张状态观测器的优点,能保证误差系统的稳定性,并具有很强的抗扰动能力,给出了控制器的详细设计过程和原理框图,并进行了数值仿真验证。     

一类复杂控制系统分散自适应鲁棒控制器设计

基于模糊逻辑系统具有充分利用语言信息和逼近连续函数性质的思想,分析研究了一类非线性不确定复杂系统的自适应控制问题.利用系统的数学模型和模糊逻辑系统对不确定性的输出信息,设计出了复杂系统的分散自适应鲁棒控制器和模糊逻辑系统参数估计的自适应律,在较弱的假设条件下,证明了这种控制器使被控系统的状态及参数估计误差一致终极有界.仿真实例表明,所提出的方法是有效的.     

间隙度量与跟踪系统中的鲁棒控制器设计

为定量研究鲁棒控制器允许对象有尽可能大的不确定性.在引入间隙度量的基础上,定义了跟踪系统鲁棒控制器的鲁棒边界,并对某跟踪系统设计了基于间隙度量的鲁棒控制器.该控制器能兼顾对象的不确定性与控制器的不确定性.由仿真结果可以看出,与普通的PID控制器相比,具有较大鲁棒边界的鲁棒控制器不仅具有较强的干扰抑制能力.而且能够在模型加性不确定性存在的情况下具有很好的跟踪性能.     

一种完全数据驱动的子空间辨识与鲁棒预测控制器设计

针对线性时变多变量系统,在可能存在输入输出数据噪声的情况下,不需已知系统的先验结构信息,提出一种完全数据驱动的子空间辨识及控制器设计方法.在子空间在线辨识基础上,利用不确定性模型更好地建模被控系统,结合鲁棒控制策略进行预测控制器的设计;将系统建模与鲁棒控制器的设计包含在一个控制系统设计框架内,对模型不确定性具有更好的鲁棒性;最后给出仿真实例验证算法的有效性.     

Design of a discrete robust controller using a first-order model approximation

In this paper, a discrete controller with integral action is designed for a linear time invariant stable process based upon a first-order model approximation. Sufficient conditions in the form of simple inequalities are derived to ensure asymptotic stability. It is shown that this condition becomes both necessary and sufficient in the special case where the control interval approaches the open-loop settling time. The stability criterion is a closed-form inequality equation that is well suited for real-time calculation of the admissible controller parameter space.     

TCSC鲁棒自适应控制器的非线性逆推设计

设计了一种应用于互联电网的TCSC鲁棒自适应调制控制器(RAMC).该控制器采用广域测量系统中的全局信号,旨在对各区域的惯量中心进行控制并保持同步运行.采用反推法推导了控制规律,并在2区域4机系统中进行了控制器性能检测.仿真结果显示,该控制器可有效阻尼互联电力系统间的机电振荡,与传统的控制器相比具有良好的性能.