A gain‐scheduled control algorithm for input constrained systems to track time‐varying references using controller state resets

In this paper, we propose a control law for a discrete‐time linear system with actuator saturation to track time‐varying reference signals. The proposed control law consists of a feedback controller and a target recalculation mechanism. The feedback controller includes an integrator to achieve zero steady‐state error in the case where the reference signal is constant. The feedback gains of the controller are parameterized by a single scheduling parameter. In the proposed control algorithm, when the tracking error is large, a modified reference signal is computed by the target recalculation mechanism so that feasibility of the algorithm and stability of the control system are guaranteed at all times. At this stage, the controller state is modified online so that the tracking control performance is improved. Further, when the tracking error becomes small, the scheduling parameter and the controller state are updated simultaneously so that the tracking control performance is improved. The problems of determining the scheduling parameter, the controller state, and the modified reference signal are reduced to convex optimization problems with linear matrix inequality constraints. The effectiveness of the proposed control method is shown through an experiment. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Constrained MPC to track time‐varying reference signals: Online optimization of virtual reference signals and controller states

In this paper, we propose a model predictive control (MPC) algorithm for linear systems with constraints to track time‐varying reference signals. The proposed controller is assumed to have an integrator as a servo compensator. In the proposed control approach, the value of the integrator state is optimally initialized at each sampling time to improve tracking control performance until the cost function becomes sufficiently small. Moreover, while the cost function is sufficiently small, the integral action is used to achieve offset‐free tracking. The control algorithm is reduced to a convex optimization problem with linear matrix inequality constraints. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Decentralized model predictive‐based load‐frequency control in an interconnected power system concerning wind turbines

This paper presents a load‐frequency control (LFC) design using the model predictive control (MPC) technique in a multi‐area power system in the presence of wind turbines (WTs). In the studied system, the controller of each local area is designed independently such that the stability of the overall closed‐loop system is guaranteed. A frequency response model of the multi‐area power system including WTs is introduced, and physical constraints of the governors and turbines are considered. The model was employed in the MPC structures. Digital simulations for a two‐area power system are provided to validate the effectiveness of the proposed scheme. The results show that with the proposed MPC technique the overall closed‐loop system performance shows robustness in the face of uncertainties due to governor and turbine parameter variation and load disturbances. A performance comparison between the proposed controller with WTs and MPC without WTs and a classical integral control scheme is carried out, confirming the superiority of the proposed MPC technique with WTs. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

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.     

Nonaveraged control‐oriented modeling and relative stability analysis of DC‐DC switching converters

This paper presents a unified and exact nonaveraged approach to derive a frequency‐domain control‐oriented model for accurate prediction of the fast timescale dynamics and performances of switching converters with fixed frequency naturally sampled pulse width modulation and integrating feedback loop. Because the approach avoids averaging and approximations related to this process, a very good accuracy of the derived model is obtained. The main difference between the presented approach and the existing methodology for accurately predicting the behavior of switching converters is that, here, we break the feedback loop and we focus on analyzing the open‐loop gain and the effect of the system parameters on relative stability. This results in an approach much similar to control systems techniques rather than nonlinear dynamical system approaches. Consequently, the relative stability is tackled easily in the frequency domain. In particular, by treating the modulator as a gain depending on the operating point, the new model is formulated in such a way that standard control‐oriented tools such as Bode diagrams and root‐loci can be easily used. Therefore, the proposed approach gives some important issues like gain and phase margins that are highly useful in controller design. It is noticed that the crossover frequency, gain, and phase margins predicted by using the averaged model may deviate significantly from the actual values given by the proposed approach. The paper points out the sources of discrepancies and the theoretical results are validated by simulations using a circuit‐level switched model.     

Dual high‐gain‐based adaptive output‐feedback control for a class of nonlinear systems

We propose an adaptive output‐feedback controller for a general class of nonlinear triangular (strict‐feedback‐like) systems. The design is based on our recent results on a new high‐gain control design approach utilizing a dual high‐gain observer and controller architecture with a dynamic scaling. The technique provides strong robustness properties and allows the system class to contain unknown functions dependent on all states and involving unknown parameters (with no magnitude bounds required). Unlike our earlier result on this problem where a time‐varying design of the high‐gain scaling parameter was utilized, the technique proposed here achieves an autonomous dynamic controller by introducing a novel design of the observer, the scaling parameter, and the adaptation parameter. This provides a time‐invariant dynamic output‐feedback globally asymptotically stabilizing solution for the benchmark open problem proposed in our earlier work with no magnitude bounds or sign information on the unknown parameter being necessary. Copyright © 2007 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.     

Multiple characteristic model‐based golden‐section adaptive control: Stability and optimization

The characteristic model‐based golden‐section adaptive control (CM‐GSAC) law has been developed for over 20 years in China with a broad range of applications in various fields. However, quite a few theoretical problems remain open despite its satisfying performance in practice. This paper revisits the stability of the CM‐GSAC from its very beginning and explores the underlying implications of the so‐called golden‐section parameter l₂≈0.618. The closed‐loop system, which consists of the CM and the GSAC, is a discrete time‐varying system, and its stability is discussed from three perspectives. First, attentions have been paid to select the optimal controller coefficients such that the closed‐loop system exhibits the best transient performance in the worst case. Second, efforts are made to improve the robustness in the presence of parameter estimation errors, which provide another choice when designing the adaptive controller. Finally, by measuring the slowly time‐varying nature in an explicit inequality form, a bridge is built between the instantaneous stability and the time‐varying stability. In order to relax the constraints on the parameter bounds of the CM, the GSAC is further extended to multiple CMs, which shows more satisfying tracking performance than that of the traditional multiple model adaptive control method. Copyright © 2014 John Wiley & Sons, Ltd.     

基于参数局部最优化理论的电励磁直线同步电机自适应速度控制

建立适合速度控制器设计的电励磁直线同步电机连续时间数学模型,通过合理的假设建立初级电枢交轴电压与初级机械速度之间的单输入单输出传递函数。采用局部参数最优化梯度法设计了自适应速度控制器,仅含有一个积分器、一个乘法器以及2个比例单元。自适应速度控制器无传统控制器的电流内环加快了响应速度,简化了系统结构。利用MATLAB数值计算软件仿真所设计的控制器,分析自适应增益调节系数与广义误差反馈系数等因素对自适应速度控制系统稳定性与收敛性的影响,仿真结果验证了该自适应速度控制策略的有效性。     

A convex optimization approach to adaptive stabilization of discrete‐time LTI systems with polytopic uncertainties

This paper suggests a simple convex optimization approach to state‐feedback adaptive stabilization problem for a class of discrete‐time LTI systems subject to polytopic uncertainties. The proposed method relies on estimating the uncertain parameters by solving an online optimization at each time step, such as a linear or quadratic programming, and then, on tuning the control law with that information, which can be conceptually viewed as a kind of gain‐scheduling or indirect adaptive control. Specifically, an admissible domain of stabilizing state‐feedback gain matrices is designed offline by means of linear matrix inequality problems, and based on the online estimation of the uncertain parameters, the state‐feedback gain matrix is calculated over the set of stabilizing feedback gains. The proposed stabilization algorithm guarantees the asymptotic stability of the overall closed‐loop control system. An example is given to show the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Reduced‐order robust adaptive control design of uncertain SISO linear systems

In this paper, a stability and robustness preserving adaptive controller order‐reduction method is developed for a class of uncertain linear systems affected by system and measurement noises. In this method, we immediately start the integrator backstepping procedure of the controller design without first stabilizing a filtered dynamics of the output. This relieves us from generating the reference trajectory for the filtered dynamics of the output and thus reducing the controller order by n, n being the dimension of the system state. The stability of the filtered dynamics is indirectly proved via an existing state signal. The trade‐off for this order reduction is that the worst‐case estimate for the expanded state vector has to be chosen as a suboptimal choice rather than the optimal choice. It is shown that the resulting reduced‐order adaptive controller preserves the stability and robustness properties of the full‐order adaptive controller in disturbance attenuation, boundedness of closed‐loop signals, and output tracking. The proposed order‐reduction scheme is also applied to a class of single‐input single‐output linear systems with partly measured disturbances. Two examples are presented to illustrate the performance of the reduced‐order controller in this paper. Copyright © 2007 John Wiley & Sons, Ltd.     

Frequency Regulation in Hybrid Power System Using Iterative Proportional-Integral-Derivative H ∞ Controller

This study considers frequency regulation in a hybrid power system consisting of conventional and distributed generation resources. The performance of two controllers—an H _∞ design via linear matrix inequalities and an iterative proportional-integral-derivative H _∞ via linear matrix inequalities—is assessed to maintain frequency deviation profile in acceptable limits. In the latter control design, the iterative linear matrix inequality approach is used to tune proportional-integral-derivative controller parameters subjected to H_∞ constraints in terms of the iterative linear matrix inequality. The efficacy of the control law and disturbance accommodation properties is shown. The robustness of these controllers is demonstrated in the hybrid power system with different load disturbance conditions, wind power, and parameter variations. Controller performance is compared with a suboptimal controller to demonstrate its superiority. It is found that the second controller design has satisfactory disturbance rejection properties and robustness against parameter variations over a wide range of conditions.     

永磁直线伺服系统最优参数负载扰动补偿方法

对于直接驱动永磁直线伺服系统,负载扰动和系统参数的变化严重影响系统伺服性能。本文提出了一种位置控制器与负载扰动补偿器相结合的扰动抑制方法,该方法同时兼顾了直线伺服系统快速的瞬时响应和良好的抗干扰能力。其中位置控制器决定系统的瞬时响应特牲,而负载扰动补偿器则用来改善系统的抗干扰能力。在负载扰动补偿器的参数确定中提出利用Parseval定理中信号在时间域内的总能量与频域内的总能量相等的原理,将位置偏差量的时域性能指标转为频域性能指标,再通过对劳斯-赫尔维茨(Routh-Hurwitz)二维数组的计算,确定最优化PI参数。仿真结果与实验表明,该补偿方法使直线电机伺服系统具有良好的控制精度与鲁棒性。     

考虑饱和环节的自动发电控制时滞系统串级控制

自动发电控制(AGC)调节过程中存在发电机变化率约束、时延等约束条件,使得基于线性模型的AGC控制策略不能反映真实电力系统的频率调节特性。针对AGC时滞系统同时存在饱和与时延的问题,提出了一种基于内外环比例—积分(PI)稳定域的串级控制系统遗传优化策略。基于AGC系统的负荷频率控制与机组控制组成的串级控制回路,采用Hopf分岔代数判据和时滞系统稳定域理论,分别求取了内外回路的PI稳定域,证明了饱和及时延参数会影响到PI稳定域的变化。通过将稳定域转化为控制器参数优化的约束条件后,对内环优化采用不同指标进行对比,证明了绝对误差积分(IAE)指标对于扰动具有更好的抑制能力;而对外环的对比表明采用时间乘平方误差积分(ITSE)指标具有更小的波动量。遗传优化结果表明所提控制策略能够有效抑制饱和及时延环节对系统性能的影响。     

A new command governor architecture for transient response shaping

In this paper, we develop a control framework for stabilization and command following of nonlinear uncertain dynamical systems. The proposed methodology consists of a new command governor architecture and an adaptive controller. The command governor is a dynamical system that adjusts the trajectory of a given command to follow an ideal reference system capturing a desired closed‐loop dynamical system behavior in transient time. Specifically, we show that the controlled nonlinear uncertain dynamical system can approach the ideal reference system by choosing the design parameter of the command governor. In addition, an adaptive element is used to asymptotically assure that the error between the controlled nonlinear uncertain dynamical system and the ideal reference system is reduced in long term. Therefore, the proposed methodology not only has closed‐loop transient and steady‐state performance guarantees but can also shape the transient response by adjusting the trajectory of the given command with the command governor. We highlight that there exists a trade‐off between the adaptive controller's learning rate and the command governor's design parameter. This key feature of our framework allows rapid suppression of system uncertainties without resorting to a high learning rate in the adaptive controller. Furthermore, we discuss the robustness properties of the proposed approach with respect to high‐frequency dynamical system content such as measurement noise and ∕ or unmodeled dynamics. A numerical example is provided to demonstrate the efficacy of the proposed architecture. Copyright © 2012 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.     

Model‐free fault‐tolerant control approach for uncertain state‐constrained linear systems with actuator faults

This paper investigates the robust adaptive fault‐tolerant control problem for state‐constrained continuous‐time linear systems with parameter uncertainties, external disturbances, and actuator faults including stuck, outage, and loss of effectiveness. It is assumed that the knowledge of the system matrices, as well as the upper bounds of the disturbances and faults, is unknown. By incorporating a barrier‐function like term into the Lyapunov function design, a novel model‐free fault‐tolerant control scheme is proposed in a parameter‐dependent form, and the state constraint requirements are guaranteed. The time‐varying parameters are adjusted online based on an adaptive method to prevent the states from violating the constraints and compensate automatically the uncertainties, disturbances, and actuator faults. The time‐invariant parameters solved by using data‐based policy iteration algorithm are introduced for helping to stabilize the system. Furthermore, it is shown that the states converge asymptotically to zero without transgression of the constraints and all signals in the resulting closed‐loop system are uniformly bounded. Finally, two simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Proposal of FCbT Considering Closed‐Loop Stability at Each Parameter Update

We propose a controller tuning method that considers closed‐loop stability after controller tuning without a mathematical plant model. We propose fictitious correlation‐based tuning that yields reasonable controller parameters using a small amount of input and output data. However, closed‐loop stability after controller tuning is not guaranteed in this approach. In this investigation, we impose a stability constraint on the parameter update in order to maintain closed‐loop stability at each parameter update. Further, by introducing particle swarm optimization instead of the Gauss–Newton method to solve the constrained nonlinear optimization problem, the initial value dependence is considerably reduced. The effectiveness of the proposed method is confirmed by a numerical example and experimental results.     

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.     

Robust H-infinity load frequency control in hybrid distributed generation system

This paper presents a study on isolated hybrid distributed generation (DG) system for improving the frequency deviation profile. The hybrid DG system consists of wind turbine generator (WTG), diesel engine generator (DEG), aqua-electrolyzer (AE), fuel cell (FC) along with energy storage units. The frequency control problem is addressed for DG system connected with superconducting magnetic energy storage (SMES) or ultra-capacitor (UC). The particle swarm optimization (PSO) based loop shaping of H-infinity controller is used and compared with those obtained by genetic algorithm (GA) to minimize the frequency deviation. The frequency stabilizing performance is analyzed under different disturbances. Also, the controller robustness in terms of system parameter uncertainties is tested for changes in parameter up to ±30% from its nominal value. The results demonstrate minimum frequency deviation as achieved by proposed controller with use of UC in hybrid DG system.