Adaptive performance/ robust control design using orthotopic set membership identification for low-dimensional systems

The adaptive robust control design problem for low-dimensional systems is addressed in this paper. The proposed scheme consists of an orthotopic set membership identifier, a robust stabilizing controller and a pole placement controller. The identifier provides the minimum (volume-wise) orthotopic region of parameters which is consistent with the data and model structure. Based on this orthotope, the robust controller computes the feasible set of stabilizing controller gains. Subsequently a pole assignment controller selects a subset from the stabilizing gains in order to place the closed-loop poles deeper inside the unit disc. Simulation studies are offered to validate the efficiency of the proposed method. © 1997 John Wiley & Sons, Ltd.     

Fully parameterized fixed‐order controller design for H∞ loop shaping method using frequency responses—extension to MIMO systems

Robust control is often applied to systems with uncertainties and disturbances. Above all, the H∞ loop shaping method is known to achieve good control performance and robustness. In this method, the final controller consists of weighting functions and a stabilizing controller. The stabilizing controller is derived for the shaped plant to suppress the H∞ norm of the transfer matrix consisting of a sensitivity function, a complementary sensitivity function, and so on. In addition, the stabilizing controller improves robust stability margin while keeping gain characteristic of the shaped plant if weighting functions are suitable. As a result, the closed‐loop system is well‐balanced between good tracking and robustness. However, a final controller tends to be high‐order. For this problem, reduction techniques are often applied to the final controller. In this case, performance and stability is not always adequately evaluated due to errors by the controller reduction. This paper proposes a fully parameterized fixed‐order controller design method using frequency responses of the plant. We formulate a design problem for multi‐input–multi‐output systems as an optimization problem. Therefore, we can directly design a low‐order controller from frequency responses using the iterative LMI optimization. Accordingly, we can avoid to deteriorate the evaluation of performance and stability.     

Data‐driven model reference control with asymptotically guaranteed stability

This paper presents a data‐driven controller tuning method that includes a set of constraints for ensuring closed‐loop stability. The approach requires a single experiment and can also be applied to nonminimum‐phase and unstable systems. The tuning scheme generates an estimate of the closed‐loop output error that is used to minimize an approximation of the model reference control problem. The correlation approach is used to deal with the influence of measurement noise. For linearly parameterized controllers, this leads to a convex optimization problem. A sufficient condition for closed‐loop stability is introduced, which can be included in the optimization problem for control design. As the data length tends to infinity, closed‐loop stability is guaranteed. The quality of the estimated controller is analyzed for finite data length. The effectiveness of the proposed method is demonstrated in simulation as well as experimentally on a laboratory‐scale mechanical setup. Copyright © 2010 John Wiley & Sons, Ltd.     

Free‐weighting matrices‐based robust wide‐area FACTS control design with considering signal time delay for stability enhancement of power systems

This paper presents a free‐weighting matrix (FWM) method based on linear control design approach for the wide‐area robust damping (WARD) controller associated with flexible AC transmission system (FACTS) device to improve the dynamical performance of the large‐scale power systems. First, the linearized reduced‐order plant model is established, which efficiently considers the time delay of the remote feedback signals transmitted by wide‐area measurement systems. Then, based on the robust control theory, the design of the FACTS‐WARD controller is formulated as the standard control problem on delay‐dependent state‐feedback robust control, which is described by a set of linear matrix inequality constraints. Furthermore, in order to obtain the optimal control parameters that can endure the maximum time delay, a FWM approach is proposed to solve the time‐dependent problem of the time‐delay system. Meanwhile, an iterative algorithm based on cone complementary linearization is presented to search out the optimal control parameters. Finally, the nonlinear simulations on the 2‐area 4‐machine and the 5‐area 16‐machine test systems are performed, to evaluate the control performance of the proposed robust wide‐area time‐delay control approach. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

线性控制系统按稳定度配置极点的一种方法

本文提出了按稳定度配置极点的一种方法。该方法把闭环系统的全部极点配置在复平面左半面的一个特定的区域之内,使闭环系统具有预期的稳定度。它定义闭环系统的主极点实部作为目标函数,用最优化方法中的直接搜索法优化搜索反馈矩阵,使其满足对目标函数的要求。此方法不仅可用于能控能观测系统的设计,而且可用于能稳定系统的设计。该方法还具有容易准备和计算时间短等优点。     

Robust adaptive control of nonlinearly parameterized systems with unmodeled dynamics

Many physical systems such as biochemical processes and machines with friction are of nonlinearly parameterized systems with uncertainties. How to control such systems effectively is one of the most challenging problems. This paper presents a robust adaptive controller for a significant class of nonlinearly parameterized systems. The controller can be used in cases where there exist parameter and nonlinear uncertainties, unmodeled dynamics and unknown bounded disturbances. The design of the controller is based on the control Lyapunov function method. A dynamic signal is introduced and adaptive nonlinear damping terms are used to restrain the effects of unmodeled dynamics, nonlinear uncertainties and unknown bounded disturbances. The backstepping procedure is employed to overcome the complexity in the design. With the proposed method, the estimation of the unknown parameters of the system is not required and there is only one adaptive parameter no matter how high the order of the system is and how many unknown parameters there are. It is proved theoretically that the proposed robust adaptive control scheme guarantees the stability of nonlinearly parameterized system. Furthermore, all the states approach the equilibrium in arbitrary precision by choosing some design constants appropriately. Simulation results illustrate the effectiveness of the proposed robust adaptive controller. __________ Translated from Journal of Sichuan University (Engineering Science Edition), 2005, 37(5): 148–153 (in Chinese)     

A heuristic‐based design of robust SMES controller taking system uncertainties into consideration

In this paper, a heuristic‐based design of robust superconducting magnetic energy storage (SMES) controller is proposed taking system uncertainties into consideration. The SMES model with active and reactive power controllers is used. In addition, the effect of SMES coil current is also included in the model. The power system and the SMES unit with the designed controller are formulated as an optimization problem. The proposed objective function considers both the damping performance index and the robust stability index. In particular, the robust SMES controller is designed to enhance the system damping performance and robustness against system uncertainties such as various load and system parameter changes. The robust stability margin is guaranteed in terms of the multiplicative stability margin (MSM). In the proposed method, the robust SMES active and reactive power controllers are designed systematically by using hybrid tabu search and evolutionary programming, so that the desired damping performance and the best obtainable MSM are acquired. Finally, the designed SMES controller is examined under different situations to evaluate and confirm the effectiveness and robustness via eigenvalue analysis and nonlinear simulations. © 2006 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Robust adaptive sliding mode control for uncertain delta operator systems

In this paper, a robust adaptive sliding mode controller is presented for delta operator systems with mismatched uncertainties and exogenous disturbances. The parameters of the delta operator system are taken for norm‐bounded uncertainties. The exogenous disturbance is also assumed to be bounded. After the statement of a sufficient condition for the existence of linear sliding surface based on linear matrix inequality technique, a robust reaching motion control method for delta operator systems is presented. Afterwards, an adaptive sliding mode controller for delta operator systems is designed. A bridge between the robust adaptive sliding mode control and the delta operator system framework is made. Numerical example is given to illustrate the effectiveness of the developed techniques. Copyright © 2009 John Wiley & Sons, Ltd.     

Guaranteed cost control with pole constraints for uncertain discrete-time switched systems

For a class of discrete-time switched systems with norm-bounded uncertainties and a quadratic cost index, the problem of designing a guaranteed cost state feedback controller with pole constraints is considered. A sufficient condition on the existence of robust guaranteed controllers is derived by a quadratic Lyapunov function approach together with linear matrix inequality (LMI) technique. Based on a constructed switching law, the closed-loop system is quadratic D-stable and the closed-loop cost function value is not more than a specified upper bound. Furthermore, the design of suboptimal guaranteed cost controllers is turned into a convex optimization problem with linear matrix inequalities constraints. A numerical example demonstrates the effect of the proposed design approach. __________ Translated from Control and Decision, 2007, 22(11): 1269–1273 [译自: 控制与决策]     

基于鲁棒方差优化的电力系统频率控制研究

随着新能源发电大规模并网,随机负荷扰动给电力系统稳定优化运行提出了新的挑战。针对自动发电控制过程中存在的随机扰动和参数摄动的问题,提出了一种基于鲁棒方差约束的状态反馈控制器的参数优化方法。根据鲁棒方差控制(Robust Variance Control,RVC)中不等式约束条件,分析了闭环系统在抑制随机扰动和提高阶跃扰动响应动态性能之间的博弈关系。构造了融合稳态状态方差和控制能量输出约束的优化问题,利用线性矩阵不等式(Linear Matrix Inequality,LMI)获得了鲁棒方差控制器参数。在此基础上,对配置的区域极点圆心坐标值和正标量两个参数进行遗传优化,得到性能指标最优的控制策略。以两区域电力系统模型为例,表明该方法能够有效抑制随机扰动并保持良好的控制性能和鲁棒性能。     

Passivity‐based sliding mode control for nonlinear systems

Passivity with sliding mode control for a class of nonlinear systems with and without unknown parameters is considered in this paper. In fact, a method for deriving a nonlinear system with external disturbances to a passive system is considered. Then a passive sliding mode control is designed corresponding to a given storage function. The passivity property guarantees the system stability while sliding mode control techniques assures the robustness of the proposed controller. When the system includes unknown parameters, an appropriate updated law is obtained so that the new transformed system is passive. The passivation property of linear systems with sliding mode is also analysed. The linear and nonlinear theories are applied to a simple pendulum model and the gravity‐flow/pipeline system, respectively. Copyright © 2008 John Wiley & Sons, Ltd.     

Automatic tuning of robust constrained cross‐direction controllers

The paper machine cross‐directional (CD) process is a large‐scale spatially distributed system. It is known to be severely ill‐conditioned as the gain rolls down to zero for some of the process directions. Model uncertainties in the process are inevitable resulting in a challenging robust control design problem. CD actuators are subject to min–max constraints while slice lip actuators are subject to additional bending moment limits. Because of the large number of input constraints, the industrial practice is to tune the CD controller assuming inactive constraints. The robustness of CD feedback loops to model uncertainties under constrained internal model control satisfies an integral quadratic inequality. This work develops an automatic tuning algorithm that guarantees robust stability and performance of the constrained CD feedback loop. Spatial response models are identified in a prediction error frame delivering bounds on the CD process pseudo‐singular values. The CD controller is synthesized online through a linear matrix inequalities feasibility problem taking into consideration the modal space uncertainty rising from the uncertainties in the estimated parameters and the expected variations in the dynamic response. The developed tuning technique is suitable for paper machines producing different grades of paper as the CD process spatial and dynamic responses change for each grade. The performance of the tuned constrained internal model control controller is validated through comparing it to an industrial CD controller that has been implemented in paper mills as part of a commercial product. Copyright © 2015 John Wiley & Sons, Ltd.     

A design method of a generalized predictive control system based on parametrization of two‐degree‐of‐freedom integral controllers

A new design method for a generalized predictive control (GPC) system based on parametrization of two‐degree‐of‐freedom integral controllers has been proposed. The objective is to guarantee stability of the control system without depending on the design parameters and to achieve low sensitivity against the plant perturbation and the disturbance. The design procedure consists of two steps. First, we design a basic integral controller for a nominal plant using the linear quadratic Gaussian (LQG) method and parametrize a class of two‐degree‐of‐freedom stabilizing controllers. Next, we tune the feedforward controller to incorporate the GPC method into our control structure. A numerical example is presented to show the effectiveness of the proposed method by comparing it with the conventional GPC method. © 1999 Scripta Technica, Electr Eng Jpn, 129(2): 62–70, 1999     

输入受限的非线性系统模型预测控制

基于模糊T—S模型对输入受限的非线性离散系统,提出了模型预测控制,导出了预测控制性能指标上界,将稳定性约束、输入约束变换成容易求解的线性矩阵不等式(LMIs)形式。采用了状态反馈控制器和并行补偿分布控制器(PDC),基于李雅普诺夫函数和线性矩阵不等式方法给出滚动时域优化的充分条件,证明了闭环系统的稳定性。仿真结果验证了所提方法的有效性。     

特高压直流输电系统调制研究

介绍直流调制功能研究的方法及步骤,以云广特高压直流工程为研究对象,具体进行了云广直流工程调制控制器的设计,包括调制控制器信号的选取、传递函数的选取、参数的确定等,并研究了云广直流调制控制器对南方电网安全性和稳定性的影响。     

考虑多机系统广域信号时滞影响的直流附加控制器设计

广域测量系统中由于引入信道、传输协议等环节引起的延迟经过积累将严重影响以广域信号为反馈的控制器动态性能.对此提出一种考虑广域测量系统(WAMS)中信号传输延迟的直流附加控制器.基于线性矩阵不等式方法(LMI)设计考虑时滞影响的直流附加控制器结构;基于粒子群、以控制器时滞稳定域最大为目标函数,对控制器参数进行寻优求解;最后由射影控制理论获得等效的低阶输出反馈控制器.对结果进行了时域仿真分析,并与一种未考虑时滞的控制器进行比较,所得结果均证明LMI方法设计的直流附加控制器的有效性.     

不确定关联时滞广义大系统的分散鲁棒镇定

为了研究一类不确定性关联时滞广义大系统的分散鲁棒镇定问题,根据广义系统理论,采用线性矩阵不等式方法,研究了不确定性关联时滞广义大系统的鲁棒稳定性和分散鲁棒镇定控制器设计,分别导出了不确定性关联时滞广义大系统的鲁棒稳定和分散鲁棒镇定的充分条件,且都是一组严格的线性矩阵不等式。当条件成立时给出了分散鲁棒反馈控制律的表示式,并用数值实例对所得结果加以仿真,结果表明所得方法是有效的。     

Robust adaptive control of Hammerstein nonlinear systems and its application to typical CSTR problems

This paper considers the robust adaptive control of Hammerstein nonlinear systems with uncertain parameters. The control scheme is derived from a modified criterion function which can overcome non‐minimum phase property of the linear subsystem. The parameter adaptation is performed by using a robust recursive least squares algorithm with a deadzone weighted factor. The control law compensates the model error by incorporating the unmodeled dynamics estimation. An online pole assignment technique is also presented to guarantee that Assumption 2 always holds. Rigorous theoretical analysis indicates that the parameter estimation convergence and the closed‐loop system stability can be guaranteed under mild conditions. Simulation examples including two typical continuous stirred tank reactor problems are studied to verify the effectiveness of the control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Data‐driven loop‐shaping design of PID controllers for stable plants

In this paper, a loop‐shaping design method of PID controllers is proposed for stable plants under the condition that the plant is linear time invariant and a finite‐time plant response is available. The integral gain of the PID controller is maximized subject to a stability margin constraint, and the optimal solution can be found by linear programming. A filter bank is used for extracting useful information from the finite‐time response data. Numerical examples show that this method is applicable to a wide range of plants including non‐minimum phase and/or time‐delay plants. Copyright © 2013 John Wiley & Sons, Ltd.     

Semi‐adaptive control of convexly parametrized systems with application to temperature regulation of chemical reactors

In this paper, we are interested in the problem of adaptive control of non‐linearly parametrized systems. We investigate the viability of defining a stabilizing parameter update law for the case when the plant model is convex on the uncertain parameters. We show that, when the only prior knowledge is convexity, there does not exist an adaptation law—derivable from the standard separable Lyapunov function technique of Parks—applicable for all the state space. Therefore, we propose a semi‐adaptive state feedback controller where adaptation takes place only in the region of the state space where convexity can be used to reduce parameter uncertainty. In the remaining part of the state space we freeze the adaptation and switch to a robust controller. This scheme ensures semi‐global stability for convexly parametrized non‐linear systems with matched uncertainty. The proposed controller is then applied to the problem of temperature regulation of continuous stirred exothermic chemical reactors where reaction heat is convex in the uncertain parameters. Copyright © 2001 John Wiley & Sons, Ltd.