Fuzzy model predictive control of non-linear processes using convolution models and foraging algorithms

In this paper, a fuzzy model predictive control (FMPC) approach is introduced to design a control system for nonlinear processes. The proposed control strategy has been successfully employed for representative, benchmark chemical processes. Each nonlinear process system is described by fuzzy convolution models, which comprise a number of quasi-linear fuzzy implications (FIs). Each FI is employed to describe a fuzzy-set based relation between control input and model output. A quadratic optimization problem is then formulated, which minimizes the difference between the model predictions and the desired trajectory over a predefined predictive horizon and the requirement of control energy over a shorter control horizon. The present work proposes to solve this optimization problem by employing a contemporary population-based evolutionary optimization strategy, called the Bacterial Foraging Optimization (BFO) algorithm. The solution of this optimization problem is utilized to determine optimal controller parameters. The utility of the proposed controller is demonstrated by applying it to two non-linear chemical processes, where this controller could achieve better performances than those achieved by similar competing controller, under various operating conditions and design considerations. Further comparisons between various stochastic optimization algorithms have been reported and the efficacy of the proposed approach over similar optimization based algorithms has been concluded employing suitable performance indices.     

Self-organizing fuzzy control of constant cutting force in turning

Constant force control is gradually becoming an important technique in the modern manufacturing process. Especially, constant cutting force control is a useful approach in increasing the metal removal rate and the tool life for turning systems. However, turning systems generally have nonlinear with uncertainty dynamic characteristics. Designing a model-based controller for constant cutting force control is difficult because an accurate mathematical model in the turning system is hard to establish. Hence, this study employed a model-free fuzzy controller to control the turning system in order to achieve constant cutting force control. Nevertheless, the design of the traditional fuzzy controller (TFC) presents difficulties in finding control rules and selecting an appropriate membership function. Moreover, the database and fuzzy rules of a TFC are fixed after the design step and then cannot appropriately regulate ones real time according to the system output response and the desired control performance. To solve the above problem, this work develops a self-organizing fuzzy controller (SOFC) for constant cutting force control to evaluate control performance of the turning system. The SOFC continually updates the learning strategy in the form of fuzzy rules, during the turning process. The fuzzy rule table of this SOFC can be begun with zero initial fuzzy rules which not only overcome the difficulty in the TFC design, but also establish a suitable fuzzy rules table, and support practically convenient fuzzy controller applications in turning systems control. To confirm the applicability of the proposed intelligent controllers, this work retrofitted an old lathe for a turning system to evaluate the feasibility of constant cutting force control. The SOFC has a better control performance in constant cutting force control than does the TFC, as verified in experimental results.     

Self-organizing fuzzy control of constant cutting force in turning

Constant force control is gradually becoming an important technique in the modern manufacturing process. Especially, constant cutting force control is a useful approach in increasing the metal removal rate and the tool life for turning systems. However, turning systems generally have nonlinear with uncertainty dynamic characteristics. Designing a model-based controller for constant cutting force control is difficult because an accurate mathematical model in the turning system is hard to establish. Hence, this study employed a model-free fuzzy controller to control the turning system in order to achieve constant cutting force control. Nevertheless, the design of the traditional fuzzy controller (TFC) presents difficulties in finding control rules and selecting an appropriate membership function. Moreover, the database and fuzzy rules of a TFC are fixed after the design step and then cannot appropriately regulate ones real time according to the system output response and the desired control performance. To solve the above problem, this work develops a self-organizing fuzzy controller (SOFC) for constant cutting force control to evaluate control performance of the turning system. The SOFC continually updates the learning strategy in the form of fuzzy rules, during the turning process. The fuzzy rule table of this SOFC can be begun with zero initial fuzzy rules which not only overcome the difficulty in the TFC design, but also establish a suitable fuzzy rules table, and support practically convenient fuzzy controller applications in turning systems control. To confirm the applicability of the proposed intelligent controllers, this work retrofitted an old lathe for a turning system to evaluate the feasibility of constant cutting force control. The SOFC has a better control performance in constant cutting force control than does the TFC, as verified in experimental results.     

Robust covariance control for discrete system by Takagi-Sugeno fuzzy controllers

Variances of the system states or outputs often play vital roles in the problem for performance requirements of many stochastic control systems. For linear stochastic systems, the covariance control technique has been applied to deal with the variance constrained design problem. This paper extends this technique to a class of discrete-time nonlinear perturbed stochastic systems, which are modeled by the Takagi-Sugeno (TS) fuzzy systems. By fuzzy IF-THEN rules, which represent local linear input-output relations, the nonlinear systems can be described by TS fuzzy models. According to the parallel distributed compensation (PDC) concept, the discrete-time nonlinear perturbed stochastic systems can be driven by the linear feedback gains. The purpose of this paper is to provide a method to design an output feedback fuzzy controller, which is based on the upper bound state covariance control technique and PDC concept, for the discrete-time perturbed stochastic systems using TS fuzzy models.     

H∞ output-feedback fuzzy proportional-integral control of fully delayed input/output systems

This paper presents the output-feedback fuzzy proportional-integral (PI) controller design for uncertain nonlinear systems with both fully delayed input and output. Based on the Takagi–Sugeno (T–S) fuzzy model representation, the output-feedback PI control is realized via parallel distributed PI compensation and novel LMI gain design. Although the T–S fuzzy PI controller is simple, asymptotic output regulation is assured to overcome the effect of uncertainty, state delay, and full input/output delays. When considering disturbance and measurement noise, the control performance is achieved by robust gain design. Furthermore, state observers and bilinear matrix inequality conditions are removed in this paper. Finally, time-delay Chua׳s circuit system and a continuous-time stirred tank reactor are taken as applications to show the expected performance.     

Reachable set estimation for Takagi-Sugeno fuzzy systems against unknown output delays with application to tracking control of AUVs

In this paper, we address the problem of reachable set estimation for continuous-time Takagi-Sugeno (T-S) fuzzy systems subject to unknown output delays. Based on the reachable set concept, a new controller design method is also discussed for such systems. An effective method is developed to attenuate the negative impact from the unknown output delays, which likely degrade the performance/stability of systems. First, an augmented fuzzy observer is proposed to capacitate a synchronous estimation for the system state and the disturbance term owing to the unknown output delays, which ensures that the reachable set of the estimation error is limited via the intersection operation of ellipsoids. Then, a compensation technique is employed to eliminate the influence on the system performance stemmed from the unknown output delays. Finally, the effectiveness and correctness of the obtained theories are verified by the tracking control of autonomous underwater vehicles.     

转向缸系统反馈线性化分析与系统解耦

为解决汽车转向缸加载控制中出现的诸如强位置干扰、多通道耦合、非线性等问题,将线性系统和非线性系统理论引入系统控制器的设计中,对各通道耦合问题开展了以前馈补偿为基础的解耦控制,所设计的前馈补偿结构简单,解耦网络阶次低;针对非线性问题提出了将非线性系统精确反馈线性化与最优控制相结合的方法,设计了基于精确反馈线性化的最优控制器,该方法将复杂的非线性系统问题转化为线性系统的综合问题,采用渐近输出跟踪方法实现系统控制。仿真结果表明:采用前馈补偿解耦控制器可以有效消除耦合,但当系统存在高度非线性时,仅采用前馈补偿解耦控制不能达到高品质的性能要求,而进一步设计的基于精确反馈线性化的最优控制器考虑系统非线性时,系统能快速、准确达到预置设定。     

Tuning fuzzy PD and PI controllers using reinforcement learning

In this paper, we propose a new auto-tuning fuzzy PD and PI controllers using reinforcement Q-learning (QL) algorithm for SISO (single-input single-output) and TITO (two-input two-output) systems. We first, investigate the design parameters and settings of a typical class of Fuzzy PD (FPD) and Fuzzy PI (FPI) controllers: zero-order Takagi–Sugeno controllers with equidistant triangular membership functions for inputs, equidistant singleton membership functions for output, Larsen’s implication method, and average sum defuzzification method. Secondly, the analytical structures of these typical fuzzy PD and PI controllers are compared to their classical counterpart PD and PI controllers. Finally, the effectiveness of the proposed method is proven through simulation examples.     

模糊自适应预测控制在航空发动机中的应用研究

对于航空发动机这样复杂的系统,其数学模型具有较大的不确定性,而模糊控制对于解决模型不确定性问题具有较好的优势,运用模糊控制理论就具有较好的实践意义。而且,航空发动机在实际运行中存在诸多可测与不可测的扰动,将模糊建模技术与预测控制算法相结合,采用输出误差反馈启发校正的方法,有效地降低了系统设计与实现的复杂性,提高了系统的实时性,并使得该算法的模糊预测控制在鲁棒性、动态性能等方面皆优于常规PID控制。最后,通过数字仿真,对比了经典PID控制和运用模糊自适应预测控制。仿真结果表明,文中所采用的方法有较好的效果,其证明了该方法在航空发动机控制中应用的可能性。     

H(∞) constrained fuzzy control via state observer feedback for discrete-time Takagi-Sugeno fuzzy systems with multiplicative noises

The purpose of this paper is to study the H(∞) constrained fuzzy controller design problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with multiplicative noises by using the state observer feedback technique. The proposed fuzzy controller design approach is developed based on the Parallel Distributed Compensation (PDC) technique. Through the Lyapunov stability criterion, the stability analysis is completed to develop stability conditions for the closed-loop systems. Besides, the H(∞) performance constraints is also considered in the stability condition derivations for the worst case effect of disturbance on system states. Solving these stability conditions via the two-step Linear Matrix Inequality (LMI) algorithm, the observer-based fuzzy controller is obtained to achieve the stability and H(∞) performance constraints, simultaneously. Finally, a numerical example is provided to verify the applicability and effectiveness of the proposed fuzzy control approach.     

Data-driven output-feedback fault-tolerant L2 control of unknown dynamic systems

This paper studies the data-driven output-feedback fault-tolerant L₂-control problem for unknown dynamic systems. In a framework of active fault-tolerant control (FTC), three issues are addressed, including fault detection, controller reconfiguration for optimal guaranteed cost control, and tracking control. According to the data-driven form of observer-based residual generators, the system state is expressed in the form of the measured input–output data. On this basis, a model-free approach to L₂ control of unknown linear time-invariant (LTI) discrete-time plants is given. To achieve tracking control, a design method for a pre-filter is also presented. With the aid of the aforementioned results and the input–output data-based time-varying value function approximation structure, a data-driven FTC scheme ensuring L₂-gain properties is developed. To illustrate the effectiveness of the proposed methodology, two simulation examples are employed.     

Delay-dependent fuzzy static output feedback control for discrete-time fuzzy stochastic systems with distributed time-varying delays

This paper is concerned with the delay-dependent H(∞) fuzzy static output feedback control scheme for discrete-time Takagi-Sugeno (T-S) fuzzy stochastic systems with distributed time-varying delays. To begin with, the T-S fuzzy stochastic system is transformed to an equivalent switching fuzzy stochastic system. Then, based on novel matrix decoupling technique, improved free-weighting matrix technique and piecewise Lyapunov-Krasovskii function (PLKF), a new delay-dependent H(∞) fuzzy static output feedback controller design approach is first derived for the switching fuzzy stochastic system. Some drawbacks existing in the previous papers such as matrix equalities constraint, coordinate transformation, the same output matrices, diagonal structure constraint on Lyapunov matrices and BMI problem have been eliminated. Since only a set of LMIs is involved, the controller parameters can be solved directly by the Matlab LMI toolbox. Finally, two examples are provided to illustrate the validity of the proposed method.     

Real-time random delay compensation with prediction-based digital redesign

Today’s technological demands require challenging control solutions such as real-time applications of Networked Control System (NCS). However, due to communication protocol and shared data bus, NCS experiences uncertain and unpredictable time delays in both input and output channels. These delays cause asynchronization between the controller and the plant thereby degrading the performance of closed-loop control systems. To address this problem, this paper proposes to utilize digital redesign technique to provide real-time random delay compensation.     

Active vibration control of a structure with output feedback based on simultaneous optimization design method

Recent advances in the field of control theory have enabled us to design active vibration control systems for various structures. In many studies, the controller used to suppress vibration has been synthesized for the given mathematical model of structure. In these cases, the designer has not been able to utilize the degree of freedom to adjust the structural parameters of the control object. To overcome this problem, so called “Structure/ Control Simultaneous Optimization Method” is used. In this context of view, this paper is concerned with the active vibration control of bridge towers, platforms and ocean vehicles etc. Simultaneous design method is used to achieve optimal system performance. Here, a general framework for the simultaneous design problem of output feedback case is introduced based on LMI (Linear Matrix Inequality). The simulation results show that the proposed design method achieves desirable control performance.     

Design PID controllers for desired time-domain or frequency-domain response

Practical requirements on the design of control systems, especially process control systems, are usually specified in terms of time-domain response, such as overshoot and rise time, or frequency-domain response, such as resonance peak and stability margin. Although numerous methods have been developed for the design of the proportional-integral-derivative (PID) controller, little work has been done in relation to the quantitative time-domain and frequency-domain responses. In this paper, we study the following problem: Given a nominal stable process with time delay, we design a suboptimal PID controller to achieve the required time-domain response or frequency-domain response for the nominal system or the uncertain system. An H(infinity) PID controller is developed based on optimal control theory and the parameters are derived analytically. Its properties are investigated and compared with that of two developed suboptimal controllers: an H2 PID controller and a Maclaurin PID controller. It is shown that all three controllers can provide the quantitative time-domain and frequency-domain responses.     

State and output feedback fuzzy variable structure controllers for multivariable nonlinear systems subject to input nonlinearities

This paper presents three fuzzy adaptive controllers for a class of uncertain multivariable nonlinear systems with both sector nonlinearities and dead zones: two first controllers are state feedbacks and the last controller is an output feedback. The design of the first controller concerns systems with symmetric and positive definite control–gain matrix, while the second control design is extended to the case of nonsymmetric control–gain matrix thanks to an appropriate decomposition, namely the product of a symmetric positive definite matrix, a diagonal matrix with diagonal entries +1 or ?1, and a unity upper triangular matrix. The third controller is an output feedback extension of the second controller. In this controller, a high-gain observer is incorporated to estimate the unmeasurable states. An appropriate adaptive fuzzy logic system is used to reasonably approximate the uncertain functions. A Lyapunov approach is adopted to derive the parameter adaptation laws and prove the stability of those control systems as well as the exponential convergence of their underlying tracking errors within an adjustable region. The effectiveness of the proposed fuzzy adaptive controllers is illustrated through simulation results.     

Neural network controller for robotic motion control

Since a robotic manipulator has a complicated mathematical model, it is difficult to design a control system based on the complicated multi-variable nonlinear coupling dynamic model. Intelligent controllers using fuzzy and neural network approaches do not need a real mathematical model to design the control structure and have attracted the attention of robotic control researchers recently. A traditional fuzzy logic controller does not have learning capability and it needs a lot of effort to search for the optimal control rules and the shapes of membership functions. Owing to the time-varying behaviour of the system, the required fine tracking accuracy is difficult to achieve by adjusting the fuzzy rules only. The implementation problems of neural network control are the initial training and initial transient stability. In order to improve the position control accuracy and system robustness for industrial applications, a neural controller is first trained off-line by using the input and output (I/O) data of a traditional fuzzy controller. Then the neural controller is implemented on a five-degrees-of-freedom robot with a back propagation algorithm for online adjustment. The experimental results show that this neural network controller achieved the required trajectory tracking accuracy after 15 on-line operations.     

Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO

This paper investigates the operation of a hybrid power system through a novel fuzzy control scheme. The hybrid power system employs various autonomous generation systems like wind turbine, solar photovoltaic, diesel engine, fuel-cell, aqua electrolyzer etc. Other energy storage devices like the battery, flywheel and ultra-capacitor are also present in the network. A novel fractional order (FO) fuzzy control scheme is employed and its parameters are tuned with a particle swarm optimization (PSO) algorithm augmented with two chaotic maps for achieving an improved performance. This FO fuzzy controller shows better performance over the classical PID, and the integer order fuzzy PID controller in both linear and nonlinear operating regimes. The FO fuzzy controller also shows stronger robustness properties against system parameter variation and rate constraint nonlinearity, than that with the other controller structures. The robustness is a highly desirable property in such a scenario since many components of the hybrid power system may be switched on/off or may run at lower/higher power output, at different time instants.     

New stability and stabilization conditions for nonlinear systems with time-varying delay based on delay-partitioning approach

This paper focuses on stability analysis and stabilization of nonlinear systems with interval time-varying delay, modeled by Takagi-Sugeno (T-S) fuzzy approach. To achieve more relaxation in the feasibility region, delay-partitioning approach is used for all integral terms in the Lyapunov-Krasovskii functional (LKF). A fuzzy Lyapunov function is proposed instead of non-integral term in LKF, and moreover, some slack matrices variables are offered to enlarge the design space. By doing this, new delay-dependent stability criteria are obtained. During the derivation of stability conditions, Jensen’s integral inequality is applied to deal with integral terms. Furthermore, in this paper the problem of controller design via the parallel distributed compensation (PDC) scheme is studied. Stability and stabilization conditions with less conservative are achieved in terms of linear matrix inequality (LMI). Finally, two numerical examples are presented to show the effectiveness of the proposed results.     

Model predictive control for a class of systems with isolated nonlinearity

The paper is concerned with an overall convergent nonlinear model predictive control design for a kind of nonlinear mechatronic drive systems. The proposed nonlinear model predictive control results in the improvement of regulatory capacity for reference tracking and load disturbance rejection. The design of the nonlinear model predictive controller consists of two steps: the first step is to design a linear model predictive controller based on the linear part of the system at each sample instant, then an overall convergent nonlinear part is added to the linear model predictive controller to combine a nonlinear controller using error driven. The structure of the proposed controller is similar to that of classical PI optimal regulator but it also bears a set-point feed forward control loop, thus tracking ability and disturbance rejection are improved. The proposed method is compared with the results from recent literature, where control performance under both model match and mismatch cases are enlightened.