Comment on "Discrete-time optimal fuzzy controller design: global concept approach"

In this correspondence, we show that the relationship between the finite optimal trajectory and the infinite optimal trajectory in Lemma 3 of the aforementioned paper cannot act as a theory basis for the further implementation of other theorems and the dynamic decomposition algorithm.     

Genetic algorithm-based optimal fuzzy controller design in the linguistic space

In this paper, a genetic algorithm (GA) based optimal fuzzy controller design is proposed. The design procedure is accomplished by establishing an index function as the consequent part of the fuzzy control rule. The inputs of the controller, after scaling, are utilized by the index function for computing the output linguistic value. This linguistic value can then be used to map the suitable fuzzy control actions. This proposed novel fuzzy control rule has crisp input and fuzzified output characteristics. The index function plays a role in mapping the desired fuzzy sets for defuzzification resulting in a controlled hypersurface in the linguistic space formed by the input fuzzy variables. Two types of index functions, both linear and nonlinear, are introduced for controlling systems with different degrees of nonlinearity. The parameters of the index function are obtained by applying a simple GA with a suitable fitness function. Various controlled systems result in various parameter sets depending on their dynamics. Under the acquired optimal parameter set the optimal index function can be used to generate the desired control actions. Several simulation examples are given to verify the performance of the proposed GA-based fuzzy controller.     

高超声速飞行器基于Back-stepping的离散控制器设计

根据高超声速飞行器纵向模型的特点,提出了基于Back-stepping的离散控制器设计方法.首先通过合理的简化,将飞行器的模型转化为连续非线性系统的严格反馈形式;然后采用欧拉法得到其近似的离散模型,根据近似离散模型并结合Back-stepping和反馈线性化方法,设计了高超声速飞行器的离散控制器.利用高超声速飞行器的纵向模型对算法进行仿真验证,得到了较为满意的控制效果.     

Discrete-time controller design to attenuate effects of external disturbances

This paper presents a discrete time controller to attenuate influence of external disturbances. The proposed controller elevates tracking performance by suppressing a peak of a plant input sensitivity function. The controller is computed from an inverse model of a conventional plant input sensitivity function. For a stable and casual inverse model, we introduce all-pass filters and unit delays. In addition, high pass filters are utilized to avoid amplification of high frequency disturbance, which is a different approach from traditional design methods. Experimental verifications demonstrate the effectiveness of this design method and it is confirmed that the controller suppresses the sensitivity peak and enhances tracking performance obviously.     

Multi-objective optimal design of fuzzy controller for structural vibration control using Hedge-algebras approach

In this paper, the problem of multi-objective optimal design of hedge-algebras-based fuzzy controller (HAC) for structural vibration control with actuator saturation is presented. The main advantages of HAC are: (i) inherent order relationships among linguistic values of each linguistic variable are always ensured; (ii) instead of using any fuzzy sets, linguistic values of linguistic variables are determined by an isomorphism mapping called semantically quantifying mapping (SQM) based on a few fuzziness parameters of each linguistic variable and hence, the process of fuzzy inference is very simple due to SQM values occurring in the fuzzy rule base and (iii) when optimizing HAC, only a few design variables which are above fuzziness parameters are needed. As a case study, a HAC and optimal HACs (opHACs) based on multi-objective optimization view point have been designed to active control of a benchmark structure with active bracing system subjected to earthquake excitation. Control performance of controllers is also discussed in order to shown advantages of the proposed method.     

Optimal fuzzy controller design: local concept approach

In this paper, we present a global optimal and stable fuzzy controller design method for both continuous- and discrete-time fuzzy systems under both finite and infinite horizons. First, a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers. Based on this sufficient condition, we derive a local concept approach to designing the optimal fuzzy controller by applying traditional linear optimal control theory. The stability of the entire closed-loop continuous fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal feedback continuous fuzzy system can not only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant feedback continuous fuzzy system possesses an infinite gain margin; that is, its stability is guaranteed no matter how large the feedback gain becomes. Two examples are given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties     

Digital fuzzy logic controller: design and implementation

In this paper, various aspects of digital fuzzy logic controller (FLC) design and implementation are discussed, Classic and improved models of the single-input single-output (SISO), multiple-input single-output (MISC), and multiple-input multiple-output (MIMO) FLCs are analyzed in terms of hardware cost and performance. A set of universal parameters to characterize any hardware realization of digital FLCs is defined. The comparative study of classic and alternative MIMO FLCs is presented as a generalization of other controller configurations. A processing element for the parallel FLC architecture realizing improved inferencing of MIMO system is designed, characterized, and tested. Finally, as a case feasibility study, a direct data stream architecture for complete digital fuzzy controller is shown as an improved solution for high-speed, cost-effective, real-time control applications     

Optimal fuzzy controller design in continuous fuzzy system: globalconcept approach

We propose a design method for a global optimal fuzzy controller to control and stabilize a continuous fuzzy system with free- or fixed-end point under finite or infinite horizon (time). A linear-like global system representation of continuous fuzzy system is first proposed by viewing a continuous fuzzy system in global concept and unifying the individual matrices into synthetical matrices. Based on this, the optimal control law which can achieve global minimum effect is developed theoretically. The nonlinear segmental two-point boundary-value problem is derived for the finite-horizon problem and a forward Riccati-like differential equation for the infinite-horizon problem. The stability of the closed-loop fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal closed-loop fuzzy system cannot only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant closed-loop fuzzy system possesses an infinite gain margin     

Discrete-time track following controller design using a state-space disturbance observer

This paper presents a method to design a discrete-time track following controller using a state-space disturbance observer. To improve sensitivity, an add-on state-space disturbance observer is introduced to a LQG/LTR track following controller, which does not affect the observer and state feedback poles thereby preserving the separation principle. Therefore disturbance observer design is possible to shape the sensitivity without affecting the stability of the LQG/LTR track following controller. The proposed disturbance observer is designed in state-space without disturbance model such as plant's inverse dynamics, periodic signal generator, and Q filter. Simulation and experimental results verify the effectiveness of the proposed design method using a disturbance observer.     

Repetitive controller design for optimal performance

In this paper, a repetitive controller design method is proposed for optimal performance. Firstly, to compensate for phase lag introduced by the low‐pass filter in the scheme, the dead time of the repetitive controller is modified. Secondly, a lead compensator is introduced to the repetitive controller, which not only widens the bandwidth of the low‐pass filter, but also improves system gain at high frequencies. The optimal parameters of the repetitive controller are obtained by solving two optimization problems. A numerical example is provided to illustrate the validity of the proposed method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A -based optimal finite-word-length controller design

A novel optimal Finite Word Length (FWL) controller design is proposed in the framework of μ theory. A computationally tractable close-loop stability measure with FWL implementation considerations of the controller is derived based on the μ theory, and the optimal FWL controller realizations are obtained by solving the resulting optimal FWL realization problem using linear matrix inequality techniques.     

Analysis and design of fuzzy controller and fuzzy observer

This paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the Takagi-Sugeno (T-S) fuzzy model. The main contribution of the paper is the development of the separation property; that is, the fuzzy controller and the fuzzy observer can be independently designed. A numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer     

Fuzzy network model-based fuzzy state controller design

The performance of model-based controller design relies heavily on the quality and suitability of the utilized process model. This contribution proposes a fuzzy network based nonlinear controller design methodology. Fuzzy networks are a model approach combining high approximation quality with high interpretability. The input/output (I/O) models commonly used for identification are transformed to fuzzy state-space models. Transferring and adjusting methods from linear state-space theory a control concept consisting of a fuzzy state controller and an adaptive set-point filter for nonlinear dynamic processes is deduced. The capability of the method is demonstrated for a hydraulic drive     

RLV抗扰动非线性最优控制器设计

可重复使用运载器(RLV)再入面临严重的扰动影响,对此设计一种抗扰动非线性最优控制器(ADNOC)。首先,基于时标分离原理设计快、慢双回路控制结构;其次,将角速率动态变换处理成线性形式,通过依赖状态的黎卡提方程(SDRE)优化方法获得最优控制指令;然后,设计非线性扰动观测器用于估计外界干扰,并在非线性最优控制律中进行干扰补偿。仿真实验结果表明,所设计的控制器能良好地完成姿态跟踪控制,抑制扰动对姿态控制的影响,实现RLV的最优控制性能。     

Inverse controller design for fuzzy interval systems

This paper aims at designing and analyzing an inverse controller for stable inversible (minimum phase) fuzzy interval linear and/or multilinear systems. The controller is designed from the fuzzy interval ranges of the system parameters using an /spl alpha/-cut methodology. Indeed, for a given /spl alpha/-cut of the fuzzy system parameters representing an uncertainty level, the control objective can be viewed as maintaining the system output within a tolerance envelope, around the exact trajectory, specified by the degree of preference /spl alpha/ on the fuzzy trajectory. The stability is ensured in the way that the controller restricts the system output divergence within the tolerance envelope. The validity of the proposed method is illustrated by simulation examples.     

一种新式三维模糊控制的设计方法

本文介绍设计三维模糊控制器的一种新方法，这种算法能很容易的解决三维模糊控制器在实际中遇到的难题。通过仿真实验可以看出三维模糊控制比二维模糊控制有更优良的控制品质，同时具有很强的适应性和鲁棒性。     

Design of an optimal fuzzy logic controller using response surfacemethodology

When the fuzzy logic controller (FLC)-designed based on the plant model-is applied to the real control system, satisfactory control performance may not be attained due to modeling errors from the plant model. Also, a controller that is designed under specific circumstances may not show satisfactory control performance when applied to other circumstances. In such cases, the control parameters of the controller must be adjusted to enhance control performance. Until now, the trial and error method has been used, consuming much time and effort. Also, the set of adjusted values is not guaranteed to be optimal. To resolve such problems, response surface methodology (RSM), a method of adjusting the control parameters of the controller, is suggested. This method is more systematic than the previous trial and error method, thus, optimal solutions can be provided with less tuning. First, the initial values of the control parameters are determined through the plant model and the optimization algorithm. Then designed experiments are performed in the region around the initial values, determining the optimal values of the control parameters that satisfy both the rise time and overshoot simultaneously     

An improved robust fuzzy-PID controller with optimal fuzzy reasoning.

Many fuzzy control schemes used in industrial practice today are based on some simplified fuzzy reasoning methods, which are simple but at the expense of losing robustness, missing fuzzy characteristics, and having inconsistent inference. The concept of optimal fuzzy reasoning is introduced in this paper to overcome these shortcomings. The main advantage is that an integration of the optimal fuzzy reasoning with a PID control structure will generate a new type of fuzzy-PID control schemes with inherent optimal-tuning features for both local optimal performance and global tracking robustness. This new fuzzy-PID controller is then analyzed quantitatively and compared with other existing fuzzy-PID control methods. Both analytical and numerical studies clearly show the improved robustness of the new fuzzy-PID controller.     

Takagi-Sugeno fuzzy model based indirect adaptive fuzzy observer and controller design

This paper proposes the design scheme of the alternative adaptive observer and controller based on the Takagi-Sugeno (T-S) fuzzy model. The T-S fuzzy modeling and the state feedback control technique are adopted for the simple structure. The proposed method maintains consistent performance in the presence of parameter uncertainties and incorporates linguistic fuzzy information from human operators. In addition, with the simple adaptive state feedback controller, it solves the singularity problem, which occurs in the inverse dynamics based on the feedback linearization method. Using Lyapunov theory and Lipschitz condition, the stability analysis is conducted, and the adaptive law is derived. The proposed method is applied to the stabilization problem of a flexible joint manipulator in order to guarantee its performance.     

Sum-of-squares-based fuzzy controller design using quantum-inspired evolutionary algorithm

In the field of fuzzy control, control gains are obtained by solving stabilisation conditions in linear-matrix-inequality-based Takagi–Sugeno fuzzy control method and sum-of-squares-based polynomial fuzzy control method. However, the optimal performance requirements are not considered under those stabilisation conditions. In order to handle specific performance problems, this paper proposes a novel design procedure with regard to polynomial fuzzy controllers using quantum-inspired evolutionary algorithms. The first contribution of this paper is a combination of polynomial fuzzy control and quantum-inspired evolutionary algorithms to undertake an optimal performance controller design. The second contribution is the proposed stability condition derived from the polynomial Lyapunov function. The proposed design approach is dissimilar to the traditional approach, in which control gains are obtained by solving the stabilisation conditions. The first step of the controller design uses the quantum-inspired evolutionary algorithms to determine the control gains with the best performance. Then, the stability of the closed-loop system is analysed under the proposed stability conditions. To illustrate effectiveness and validity, the problem of balancing and the up-swing of an inverted pendulum on a cart is used.