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.     

A new decoupling design of self‐tuning multivariable generalized predictive control

A novel robust decoupling method with multivariable generalized predictive control (MGPC) for a class of nonlinear systems is presented in an adaptive version. The cross‐coupling action and the non‐linear actors of the system are identified on‐line by a neural network. A feedforward compensation based on generalized predictive control, is proposed for decoupling control. A modified recursive least‐squares (RLS) algorithm can be used to estimate the linear parameters for time‐varying systems. Simulations are carried out and the results show the effectiveness of the proposed algorithm. Copyright © 1999 John Wiley & Sons, Ltd.     

A design of multivariable,self‐tuning PID controllers with an internal model structure

Self‐tuning control schemes (STC) are useful for systems with unknown or slowly time‐varying parameters. Some single‐input/single‐output PID control schemes based on STCs have been proposed for such systems. However, there are a lot of multivariable systems in real process industries. And these systems often have relatively large time delays. In this paper, a design scheme of self‐tuning PID control system is proposed for multivariable systems with unknown parameters and time delays. The controlled object is equipped with an internal model in order to compensate the time delay and also unstable zeros. Subsequently, a multivariable PID controller is designed for the augmented or compensated system. The PID parameters are calculated recursively based on the relationship between the minimum variance control law and the PID control law. A simulation example is presented to demonstrate the effectiveness of the proposed scheme. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 146(4): 58–64, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10241     

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.     

Practical aspects of self‐tuning controllers

The contribution presents a class of Single Input Single Output (SISO) discrete self‐tuning controllers suitable for industrial applications. The proposed adaptive controllers can be divided into three groups. The first group covers PID adaptive algorithms with using of traditional methods. The second group is based on polynomial solutions of control problems and the third group is derived from the use of the minimization of linear quadratic criterion. All types of algorithms were unified and incorporated into a Matlab ‐ like Toolbox for self‐tuning control. Copyright © 1999 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.     

Adaptive control of discrete‐time nonlinear systems by recurrent neural networks in quasi‐sliding mode like regime

The aim of this study was to design an adaptive control strategy based on recurrent neural networks (RNNs). This neural network was designed to obtain a non‐parametric approximation (identification) of discrete‐time uncertain nonlinear systems. A discrete‐time Lyapunov candidate function was proposed to prove the convergence of the identification error. The adaptation laws to adjust the free parameters in the RNN were obtained in the same stability analysis. The control scheme used the states of the identifier, and it was developed fulfilling the necessary conditions to establish a behavior comparable with a quasi‐sliding mode regime. This controller does not use the regular form of the switching function that commonly appears in the sliding mode control designs. The Lyapunov candidate function to design the controller and the identifier simultaneously requires the existence of positive definite solutions of two different matrix inequalities. As consequence, a class of separation principle was proven when the RNN‐based identifier and the controller were designed by the same analysis. Simulations results were designed to show the behavior of the proposed controller solving the tracking problem for the trajectories of a direct current (DC) motor. The performance of the proposed controller was compared with the solution obtained when a classical proportional derivative controller and an adaptive first‐order sliding mode controller assuming poor knowledge of the plant. In both cases, the proposed controller showed superior performance when the relation between the tracking error convergence and the energy used to reach it was evaluated. Copyright © 2016 John Wiley & Sons, Ltd.     

Sliding mode disturbance observer control based on adaptive synchronization in a class of fractional‐order chaotic systems

In this paper, a fractional‐order Dadras‐Momeni chaotic system in a class of three‐dimensional autonomous differential equations has been considered. Later, a design technique of adaptive sliding mode disturbance‐observer for synchronization of a fractional‐order Dadras‐Momeni chaotic system with time‐varying disturbances is presented. Applying the Lyapunov stability theory, the suggested control technique fulfils that the states of the fractional‐order master and slave chaotic systems are synchronized hastily. While the upper bounds of disturbances are unknown, an adaptive regulation scheme is advised to estimate them. The recommended disturbance‐observer realizes the convergence of the disturbance approximation error to the origin. Finally, simulation results are presented in one example to demonstrate the efficiency of the offered scheme on the fractional‐order Dadras‐Momeni chaotic system in the existence of external disturbances.     

Optimal and self‐tuning weighted measurement fusion Kalman filters and their asymptotic global optimality

For the multisensor linear discrete time‐invariant stochastic systems with unknown noise variances, using the correlation method, the information fusion noise variance estimators with consistency are given by taking the average of the local noise variance estimators. Substituting them into two optimal weighted measurement fusion steady‐state Kalman filters, two new self‐tuning weighted measurement fusion Kalman filters with a self‐tuning Riccati equation are presented. By the dynamic variance error system analysis (DVESA) method, it is rigorously proved that the self‐tuning Riccati equation converges to the steady‐state optimal Riccati equation. Further, by the dynamic error system analysis (DESA) method, it is proved that the steady‐state optimal and self‐tuning Kalman fusers converge to the global optimal centralized Kalman fuser, so that they have the asymptotic global optimality. Compared with the centralized Kalman fuser, they can significantly reduce the computational burden. A simulation example for the target tracking systems shows their effectiveness. Copyright © 2010 John Wiley & Sons, Ltd.     

Sliding mode disturbance observer‐based adaptive control for uncertain MIMO nonlinear systems with dead‐zone

In this paper, an adaptive integral sliding mode control (ISMC) scheme is developed for a class of uncertain multi‐input and multi‐output nonlinear systems with unknown external disturbance, system uncertainty, and dead‐zone. The research is motivated by the fact that the ISMC scheme against unknown external disturbance and system uncertainty is very important for multi‐input and multi‐output nonlinear systems. The system uncertainty, the unknown external disturbance, and the effect of dead‐zone are integrated as a compounded disturbance, which is well estimated using a sliding mode disturbance observer (SMDO). Then, the adaptive ISMC based on the designed SMDO is presented to guarantee the satisfactory tracking performance in the presence of system uncertainty, external disturbance, and dead‐zone. Finally, the designed adaptive ISMC strategy based on SMDO is applied to the attitude control of the near space vehicle, and simulation results are presented to illustrate the effectiveness of the proposed adaptive ISMC scheme using the SMDO. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal and self‐tuning fusion Kalman filters for discrete‐time stochastic singular systems

Based on the optimal fusion estimation algorithm weighted by scalars in the linear minimum variance sense, a distributed optimal fusion Kalman filter weighted by scalars is presented for discrete‐time stochastic singular systems with multiple sensors and correlated noises. A cross‐covariance matrix of filtering errors between any two sensors is derived. When the noise statistical information is unknown, a distributed identification approach is presented based on correlation functions and the weighted average method. Further, a distributed self‐tuning fusion filter is given, which includes two stage fusions where the first‐stage fusion is used to identify the noise covariance and the second‐stage fusion is used to obtain the fusion state filter. A simulation verifies the effectiveness of the proposed algorithm. Copyright © 2008 John Wiley & Sons, Ltd.     

Self‐tuning control for polynomial systems using a receding horizon observer and control strategy

A receding horizon observer and control scheme is introduced for non‐linear systems described by polynomial maps. This control scheme has a natural interpretation as a two‐stage adaptive or self‐tuning control algorithm. The non‐linear feedback that results is defined only on the basis of past input and output measurements. The computational complexity aspects of this approach to adaptive or self‐tuning control are briefly discussed. A linear system and a Hénon map example are used to illustrate the ideas. Copyright © 2004 John Wiley & Sons, Ltd.     

Adaptive finite‐time control for high‐order nonlinear systems with mismatched disturbances

In this paper, adaptive finite‐time control is addressed for a class of high‐order nonlinear systems with mismatched disturbances. An adaptive finite‐time controller is designed in which variable gains are adjusted to ensure finite‐time stabilization for the closed‐loop system. Chattering is reduced by a designed adaptive sliding mode observer which is also used to deal with the mismatched disturbances in finite time. The proposed adaptive finite‐time control method avoids calculating derivative repeatedly of traditional backstepping methods and reduces computational burden effectively. Three numerical examples are given to illustrate the effectiveness of the proposed method.     

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.     

直流伺服系统单值预估离散滑模控制

为了保证闭环系统的鲁棒稳定性,根据不确定系统的名义模型设计理想滑模面,并以名义模型作为预测模型,利用当前及过去时刻的滑模信息预测将来时刻的滑模动态,将预测控制理论中滚动优化、反馈校正的思想引入离散滑模控制系统的设计,提出了基于单值预估控制算法的离散滑模控制系统设计方法。仿真结果表明,该方法不仅完全消除了抖振现象,且能保证闭环系统的鲁棒稳定性。另外,由于采用了单值预估,使得控制算法非常简单。     

Adaptive TS‐FNN control for a class of uncertain multi‐time‐delay systems: The exponentially stable sliding mode‐based approach

This paper presents an adaptive Takagi–Sugeno fuzzy neural network (TS‐FNN) control for a class of multiple time‐delay uncertain nonlinear systems. First, we develop a sliding surface guaranteed to achieve exponential stability while considering mismatched uncertainty and unknown delays. This exponential stability result based on a novel Lyapunov–Krasovskii method is an improvement when compared with traditional schemes where only asymptotic stability is achieved. The stability analysis is transformed into a linear matrix inequalities problem independent of time delays. Then, a sliding mode control‐based TS‐FNN control scheme is proposed to achieve asymptotic stability for the controlled system. Since the TS‐FNN combines TS fuzzy rules and a neural network structure, fewer numbers of fuzzy rules and tuning parameters are used compared with the traditional pure TS fuzzy approach. Moreover, all the fuzzy membership functions are tuned on‐line even in the presence of input uncertainty. Finally, simulation results show the control performance of the proposed scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

Data‐driven tuning of linear parameter‐varying precompensators

Methods for direct data‐driven tuning of the parameters of precompensators for linear parameter‐varying (LPV) systems are developed. Since the commutativity property is not always satisfied for LPV systems, previously proposed methods for LTI systems that use this property cannot be directly adapted. When the ideal precompensator giving perfect mean tracking exists in the proposed precompensator parameterization, the LPV transfer operators do commute and an algorithm using only two experiments on the real system is proposed. It is shown that this algorithm gives consistent estimates of the ideal parameters despite the presence of stochastic disturbances. For the more general case, when the ideal precompensator does not belong to the set of parameterized precompensators, another technique is developed. This technique requires a number of experiments equal to twice the number of precompensator parameters and it is shown that the calculated parameters minimize the mean‐squared tracking error. The theoretical results are demonstrated in simulation. Copyright © 2009 John Wiley & Sons, Ltd.     

A study of decoupling with skeleton matrix in two‐degree‐of‐freedom generalized minimum variance control

There are many multi‐input multi‐output (MIMO) systems in chemical plants, and they have multiple time delays of different length in each input and output pair. This paper explains a two‐degree‐of‐freedom (2DOF) control system based on generalized minimum variance control (GMVC) for MIMO systems. It can improve the tracking performance with respect to the reference signals and the response properties for the disturbance. The states between the sampling period can be expressed by using the modified z transform to take account of multiple time delays. Additionally, a tracking controller is designed to decouple the plant. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 176(1): 28–36, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21046     

A comparison of model‐based and data‐driven controller tuning

In many industrial applications, finding a model from physical laws that is both simple and reliable for control design is a hard and time‐consuming undertaking. When a set of input/output measurements is available, one can derive the controller directly from data, without relying on the knowledge of the physics. In the scientific literature, two main approaches have been proposed for control system design from data. In the ‘model‐based’ approach, a model of the system is first derived from data and then a controller is computed‐based on the model. In the ‘data‐driven’ approach, the controller is directly computed from data. In this work, the previous approaches are compared from a novel perspective. The main finding of the paper is that, although from the standard perspective of parameter variance analysis the model‐based approach is always statistically more efficient, the data‐driven controller might outperform the model‐based solution for what concerns the final control cost. Copyright © 2013 John Wiley & Sons, Ltd.     

Stability analysis of a combined direct variable structure adaptive control – the discrete‐time case

This paper presents the proofs of robust stability of a discrete‐time robust model reference controller combined with variable structure in an adaptive framework. All the proofs of robust stability are derived for the discrete‐time case and are similar to those already existing for the conventional non‐combined case. The controller is applied to a SISO LTI plant with unmodeled dynamics of multiplicative and additive types. It is shown that the combined controller can arbitrarily improve the convergence of the error while maintaining the robustness if compared with the non–combined case. Simulation results illustrate the performance of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.