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 Controller Tuning for Nonminimum Phase Plants with Stability Constraints

This paper addresses the model reference control problem, which is a typical control problem found in data‐driven controller tuning methods. For nonminimum phase plants, the unstable zeros of the plant should be included in the reference to avoid destabilization of the resulting closed‐loop system and improve tracking performance. First, we propose a data‐driven controller tuning method with closed‐loop stability taken into consideration and with the tuned controller parameters in the time domain. If the plant has unstable zero(s), the proposed method would not lead to destabilizing controller in the worst case. Closed‐loop stability is checked using linear inequalities described with input/output data. This contributes to reducing computation in the proposed method. Moreover, this paper proposes a data‐driven controller tuning method for nonminimum phase plants estimating the unstable zero(s) using a flexible reference model at each parameter update and reflecting them into the resulting reference model. The effectiveness of the proposed method is confirmed through numerical experiments.     

Robust control and data‐driven tuning of a hybrid integrator‐gain system with applications to wafer scanners

A hybrid integrator‐gain system is discussed that aims for improved low‐frequency disturbance rejection, while, at the same time, does not deteriorate overshoot and settling times when compared with a linear integrator. The hybrid integrator has similar phase advantages as the well‐known Clegg integrator but without inducing the discontinuous behavior resulting from resetting system state values. Optimal tuning of the controller parameters of the hybrid integrator is strongly influenced by machine‐specific properties and therefore favors a data‐driven optimization approach. However, as a time‐domain optimization algorithm can easily lead to nonrobust solutions in the sense of large peaking of the closed‐loop frequency response functions, frequency‐domain robustness constraints will be imposed. By means of an adaptive weighting filter design, the parameter updates are penalized upon violation of said robustness constraints. Posed in an unconstrained problem formulation, this is subsequently solved by applying a Gauss‐Newton–based parameter update scheme. Closed‐loop stability of the linear time‐invariant plant and controller in feedback connection with a hybrid integrator‐gain system element follows from a circle‐criterion‐like analysis, which is based on evaluating (measured) frequency response data. Measurement results obtained from an industrial wafer scanner demonstrate the effectiveness of the approach.     

Recursive Gauss–Seidel algorithm for direct self‐tuning control

A recursive algorithm based on the use of Gauss–Seidel iterations is introduced to adjust the parameters of a self‐tuning controller for minimum phase and a class of nonminimum phase discrete‐time systems. The proposed algorithm is called the Recursive Gauss–Seidel (RGS) algorithm and is used to update the controller parameters directly. The use of the RGS algorithm with a generalized minimum variance control law is also given for nonminimum phase systems, and a forgetting factor is used to track the time‐varying parameters. Furthermore, the overall stability of the closed‐loop system is proven by using the Lyapunov stability theory. Using computer simulations, the performance of the RGS algorithm is examined and compared with the widely used recursive least squares algorithm.Copyright © 2011 John Wiley & Sons, Ltd.     

State‐feedback stabilization for a class of more general high order stochastic nonholonomic systems

This paper studies the problem of state‐feedback stabilization control for a class of high order stochastic nonholonomic systems with disturbed virtual control directions and more general nonlinear drifts. By using the backstepping approach, we develop a recursive controller design procedure in the stochastic setting. To get around the stabilization burden associated with nonholonomic systems, a switching control strategy is exploited in this procedure. The tuning function technique is applied in the design to avoid the disadvantage of overparameterization. It is shown that, under some conditions, the designed controller could ensure that the closed‐loop system is almost asymptotically stabilized in probability. It is noted that the obtained conclusion can be extended to multi‐input systems. A simulation example is provided to illustrate the effectiveness of the proposed approach. Copyright © 2011 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.     

On identification methods for direct data‐driven controller tuning

In non‐iterative data‐driven controller tuning, a set of measured input/output data of the plant is used directly to identify the optimal controller that minimizes some control criterion. This approach allows the design of fixed‐order controllers, but leads to an identification problem where the input is affected by noise, and not the output as in standard identification problems. Several solutions that deal with the effect of measurement noise in this specific identification problem have been proposed in the literature. The consistency and statistical efficiency of these methods are discussed in this paper and the performance of the different methods is compared. The conclusions offer a guideline on how to solve the data‐driven controller tuning problem efficiently. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust self‐tuning PI decoupling control of uncertain multivariable systems

In this paper, for a class of multivariable systems with strong couplings, a robust self‐tuning PI decoupling controller is developed by combining a self‐tuning PI controller with a feedforward decoupling compensator and a filter. To determine the gains and other parameters of the PI decoupling controller, we first introduced a reduced order model. The parameters of the reduced order model are identified by using a normalized projection algorithm with dead zone. The gains of the PI controller together with other parameters are tuned online according to the certainty equivalent principle. By resorting to time‐varying operation, we presented the bounded‐input bounded‐output stability conditions and convergence conditions of the closed‐loop system. Simulation results on a synthetic system and a twin‐tank level system show the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Open‐loop Stackelberg learning solution for hierarchical control problems

This work presents a novel framework based on adaptive learning techniques to solve the continuous‐time open‐loop Stackelberg games. The method yields real‐time approximations of the game value and convergence of the policies to the open‐loop Stackelberg‐equilibrium solution, while also guaranteeing asymptotic stability of the equilibrium point of the closed‐loop system. It is implemented as a separate actor/critic parametric network approximator structure for every player and involves simultaneous continuous‐time adaptation. To introduce and implement the hierarchical structure to the coupled optimization problem, we adjoin to the leader the controller dynamics of the follower. A persistence of excitation condition guarantees convergence of both critics to the actual game values that eventually solve the hierarchical optimization problem. A simulation example shows the efficacy of the proposed approach.     

Immersion and invariance adaptive control for discrete‐time systems in strict‐feedback form with input delay and disturbances

This work presents a new adaptive control algorithm for a class of discrete‐time systems in strict‐feedback form with input delay and disturbances. The immersion and invariance formulation is used to estimate the disturbances and to compensate the effect of the input delay, resulting in a recursive control law. The stability of the closed‐loop system is studied using Lyapunov functions, and guidelines for tuning the controller parameters are presented. An explicit expression of the control law in the case of multiple simultaneous disturbances is provided for the tracking problem of a pneumatic drive. The effectiveness of the control algorithm is demonstrated with numerical simulations considering disturbances and input‐delay representative of the application.     

Anti‐windup synthesis for a model predictive control system

In this paper, an anti‐windup design problem for a model predictive control system is studied. The plant is assumed to be stable. First, we propose the structure of an output feedback model predictive controller with an anti‐windup compensator. Then we show a design method of the anti‐windup compensator that guarantees closed‐loop stability and improves the transient response. The design problem of the anti‐windup compensator is reduced to a linear matrix inequality (LMI) optimization problem. Further, it is shown that there always exists an anti‐windup compensator that ensures global asymptotic stability. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

虚拟同步发电机稳定性分析与参数设计

在电压电流双闭环内核外级联功率控制外环构成的虚拟同步发电机(VSG)控制方案可引入惯性到逆变器中,从而增强并网后对系统稳定性的支持。针对此种VSG的参数设计和稳定性问题,提出了一种由线性化系统模型特征值灵敏度矩阵引导的VSG参数整定方法。由于级联控制回路之间的相互作用以及系统动态对控制器参数的复杂依赖性,使传统的参数整定方法在低开关频率下效果欠佳。而新方案以迭代优化的形式实现,可确保系统稳定性,并使系统特性值从关键位置处移开。最后,开展了时域对比仿真,验证了相对于传统参数设计方案,采用新方案设计的参数明显改善了VSG的动态性能。     

Active fault tolerant control systems by the semi‐Markov model approach

This paper investigates the active fault tolerant control problem via the H _∞ state feedback controller. Because of the limitations of Markov processes, we apply semi‐Markov process in the system modeling. Two random processes are involved in the system: the failure process and the fault detection process. Therefore, two corresponding semi‐Markov processes are integrated in the closed‐loop system model. This framework can generally accommodate different types of system faults, including the randomly happening sensor faults and actuator faults. A controller is designed to guarantee the closed‐loop system stability with a prescribed noise/disturbance attenuation level. The controller can be readily solved by using convex optimization techniques. A vertical take‐off and landing vehicle example with actuation faults is used to demonstrate the effectiveness of the proposed technique. Copyright © 2013 John Wiley & Sons, Ltd.     

Stability of self‐tuning control based on Lyapunov function

The overall stability of a self‐tuning controller for discrete‐time systems is proved by using the Lyapunov function in this paper, for minimum and a class of non‐minimum phase systems. The self‐tuning controller utilizes a recursive estimate algorithm for the controller parameters based on the generalized minimum variance criterion. Previously, the stability had been proved in the case of minimum phase systems. A new type of self‐tuning controller for the discrete‐time system with delay in control input is also studied which is named the generalized minimum variance criterion‐β equivalent control, and its stability is proved. The simulation is done to evaluate the performance of the proposed self‐tuning controller. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Teaching sampled‐data H∞ control theory using arm robot experiment system

This paper explains how to use an arm robot experiment system to teach sampled‐data H_∞ control theory. A design procedure is presented for a digital tracking control system for a continuous plant with structured uncertainties; the target is the positioning control of an arm robot. To guarantee the robust stability of the closed‐loop system and provide the desired closed‐loop performance, the design problem is first formulated as a sampled‐data H_∞ control problem, and is then transformed into an equivalent discrete‐time H_∞ control problem. Finally, linear matrix inequalities are used to obtain a reduced‐order output‐feedback controller and a static state‐feedback controller. In a course, the design procedure is explained and practice is provided through simulations and experiments. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

An improved adaptive backstepping approach on static var compensator controller of nonlinear power systems

The transient stability problem of a single‐machine infinite‐bus system with static var compensator is solved in this paper, where the static var compensator controller is designed by an improved backstepping method combining error compensation, adaptive backstepping control, and sliding mode variable structure control. Crucially, the error compensation term, which chooses in the step of virtual control by the adaptive backstepping method, is introduced to ensure that the system states are bounded, maintaining the nonlinearity of the power systems while also improving the speed of parameter identification. Meanwhile, the Lyapunov function is constituted step by step to achieve stability of the subsystem. In addition, a parameter updating law and a nonlinear control law are explicitly given to asymptotically stabilize the closed‐loop system. Finally, a simulation is used to illustrate the effectiveness and the practicality of the proposed control approach.     

A design method of strong stability self‐tuning controller based on on‐demand type feedback control

This paper proposes a design method of strong stability self‐tuning controller based on on‐demand type feedback control. For safety in industrial applications, although it is important to consider on‐demand type feedback control system, the previous papers about on‐demand type feedback control did not consider the influence of noise and fixed the design parameter to constant value. Therefore, this paper extends the design parameter of on‐demand type feedback control as stable rational function through the design method of strong stability system using coprime factorization. Moreover the self‐tuning controller of the proposed method is given and the control result with noise is shown by numerical example.     

Learning‐based iterative modular adaptive control for nonlinear systems

In this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach: we first design a robust nonlinear state feedback that renders the closed‐loop input‐to‐state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed‐loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data‐driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a data‐driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization‐based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data‐driven learning algorithms gives a learning‐based modular indirect adaptive controller. We show the efficiency of this approach on a two‐link robot manipulator numerical example.     

Design of an Implicit GMV‐PID Controller Using Closed Loop Data

In industrial processes, PID control has been applied in many real systems. The control performance strongly depends on the PID parameters. Although some schemes for tuning PID parameters have been proposed, these schemes need system parameters which are estimated by system identification in order to calculate the PID parameters. On the other hand, model‐free controller design schemes represented by virtual reference feedback tuning (VRFT) or FRIT have received much attention in the last few years. These methods can calculate control parameters using closed loop data and are expected to reduce computational costs. In this paper, a type of implicit PID controller using closed loop data is proposed. In the proposed method, the PID parameters are calculated on the basis of the implicit generalized minimum variance control. The control performance can be suitably adjusted by means of only a user‐specified parameter. The effectiveness of the proposed method is numerically and experimentally evaluated.