Design of Low-Cost Fuzzy Controllers with Reduced Parametric Sensitivity Based on Whale Optimization Algorithm

This paper proposes a novel application of Whale Optimization Algorithm (WOA) as solution for solving a complex control design and tuning problem concerning fuzzy control systems that control processes modeled as second-order servo systems with an integral component and variable parameters. The minimization of objective functions containing the error of the controlled process and the output sensitivity functions of the sensitivity models defined with respect to the parametric variations of the controlled process (the servo system) defines the optimization problem. WOA is integrated with the aim of obtaining optimal controller parameters therefore obtaining a new generation of Takagi-Sugeno-Kang proportional-integral fuzzy controllers. For this, a design method is defined and experimentally validated with the aid of a laboratory nonlinear servo system.

Gravitational search algorithm-based design of fuzzy control systems with a reduced parametric sensitivity

This paper presents a method for fuzzy model reference adaptive control system design for a partially known multi-input multi-output (MIMO) linear dynamic plant. Differential or convolutional equations can describe the plant to be controlled, and the fuzzy controller is assumed to be from the MIMO sector-bounded nonstationary nonlinearities class. The task is to obtain robust adaptive stabilization. Some absolute stability theorems and integral evaluations of the state and control vectors are applied in the MIMO fuzzy adaptive controller design procedure for the first time. A method for automatically obtaining a near-optimal nonlinear dynamic reference model is described. A practical step-by-step procedure of the MIMO adaptive fuzzy controller design is proposed, resulting in highly interpretable MIMO fuzzy control rules based on triangular fuzzy sets and strong triangular fuzzy partition. An example of the fuzzy controller design according to the proposed procedure is given.

In this second part of the paper on the analysis and design of uncertain fuzzy control systems, we present a controller design method for a class of uncertain fuzzy control systems. This class of systems can be represented by the discrete-time uncertain fuzzy models discussed in Part I. Since this model representation considers system uncertainties and system disturbance, the controller design problem for this kind of model becomes a H/sub /spl infin// control problem for a nonlinear uncertain system. A new stability analysis and control system design approach are then developed for this kind of uncertain fuzzy model. Furthermore, a constructive algorithm is developed to obtain the H/sub /spl infin// feedback control law.

This paper addresses the analysis and design of fuzzy control systems for a class of complex uncertain single input single output nonlinear systems. In the design procedure, we represent the nonlinear system using a Takagi-Sugeno fuzzy model and construct a global fuzzy logic controller by blending all local state feedback controllers with a sliding mode controller. Unlike the commonly used parallel distributed compensation technique, we can design a global stable fuzzy controller without finding a common Lyapunov function for all local control systems, and can obtain a good tracking performance. Furthermore, a stability analysis is carried out not for the fuzzy model but for a real nonlinear system with uncertainties. One simulation example is given to show the effectiveness and feasibility of the proposed fuzzy controller design method.

Over the past two decades, there has been a rapidly growing interest in approximating a nonlinear system by a Takagi-Sugeno (T-S) fuzzy model (Takagi & Sugeno, 1985). In general, this model is represented by using a set of fuzzy rules to describe a global nonlinear system in terms of a set of local linear models which are smoothly connected by fuzzy membership functions. Based on the T-S fuzzy model, recently, various fuzzy controllers have been developed under the so-called parallel-distributed compensation (PDC) scheme (in which each control rule is distributively designed for the corresponding rule of a T-S fuzzy model) and have been widely and successfully applied in fields ranging from aerospace to process control. The reason is because the fuzzy model-based control method provides a natural, simple and effective design approach to complement other nonlinear control techniques that require special and rather involved knowledge. Below are listed the main features of T-S model-based fuzzy control method: 1. It does not require severe structural assumptions on the plant model. 2. It preserves well-understood linear intuition. 3. It is naturally compatible with decompositions of the overall control problem. The decompositions are typically not hierarchical, and the interactions of sub-problems are captured by physical variables that are typically state variables in a more complete model of the overall system. 4. It enables control systems to respond rapidly to changing operating conditions. For this reason, it is important that the selected physical variables reflect changes in plant dynamics as operating conditions change. In fact, the T-S model-based fuzzy control method (of divide and conquer type) constructs a nonlinear controller, with certain required dynamic properties, by combining, in some sense, the members of appropriate family of linear time-invariant controllers. Here, nonlinear control design task is broken into a number of linear sub-problems, which enable linear design methods to be applied to nonlinear problems. Within the general framework of the T-S fuzzy model-based control method, a flurry of research activities have quickly yielded many important results on the design of fuzzy control systems by means of the following Lyapunov function approaches: 1. Common quadratic Lyapunov function approach (Tanaka & Sugeno, 1992; Tanaka et al, 1996; Wang et al, 1996; Cao & Frank, 2000; Assawinchaichote, 2004).

The paper discusses the controller design for a class of fuzzy systems. A new method is developed for the design of fuzzy control systems. The basic idea of this new method is to represent the fuzzy system in a family of local state space models, and then to construct a global controller by considering each local state feedback controller. It is shown that this controller guarantees global stability of the closed loop fuzzy system. The issue of a state observer for the fuzzy system is also addressed. A numerical example is given for demonstration of the performance of the method. >

In this paper, a method for the automatic design of Fuzzy Control Systems is introduced. The method is based on the identification of the inverse model of the process to be controlled by using a Neural Network. The Neural Network which models the inverse process, is used again to obtain a set of tuples representing the fuzzy variables of the fuzzy controller. In order to obtain the fuzzy linguistic variables involved in the fuzzy controller, a Neural Network is used with the DCL algorithm. Finally, the fuzzy controller is implemented by a decision table. The method has been applied to the automatic development of a fuzzy controller for a highly non linear process.

Fuzzy logic control based on the Takagi–Sugeno inference method has been applied for the yeast alcoholic fermentation running in a continuous-time biochemical reactor in this paper. A type-1 fuzzy PID controller was designed to temperature control in a biochemical reactor. The fuzzy PID controller was also designed using type-2 fuzzy sets. The advantage of the fuzzy control is that it can be used very successfully for control of strongly non-linear processes and processes that are difficult to model because of complicated reaction kinetics. Obtained simulation results confirm this fact. The disadvantage of the fuzzy control design lies in the time-consuming tuning of controllers. The subtractive clustering method was used to identify the rule base. This approach was chosen to minimize the number of rules of the designed fuzzy logic controllers and to simplify the fuzzy controller design. Simulation results confirm that fuzzy PID controllers can assure better performance than conventional PID controllers. Yeast alcoholic fermentation is an exothermic process and the cooling is necessary to maintain the optimal temperature in the reactor. Fuzzy PID control reduces coolant consumption in comparison with conventional PID control and so it assures energy-efficient control of continuous-time alcoholic fermentation. Using type-2 fuzzy sets in the fuzzy PID controller design is very promising as the type-2 fuzzy controller offers even better results than the type-1 fuzzy controller.

In this paper, a class of fuzzy stochastic control systems with random delays is examined. The fuzzy rule base used consists of a collection of r fuzzy IF-THEN rules defined as a function of the conditional variable. The method of theory of invariant cones is used to design a class of local fuzzy control law. A verifiable sufficient condition for stochastic stability of the fuzzy stochastic delay differential equation is given.

In order to meet the requirements of high precision and fast response of permanent magnet direct drive (PMDD) wind turbines, this paper proposes a fuzzy proportional integral (PI) controller associated with a new control strategy for wind turbine converters. The purpose of the control strategy is to achieve the global optimization for the quantization factors, ke and kec, and scale factors, kup and kui, of the fuzzy PI controller by an improved particle swarm optimization (PSO) method. Thus the advantages of the rapidity of the improved PSO and the robustness of the fuzzy controller can be fully applied in the control process. By conducting simulations for 2 MW PMDD wind turbines with Matlab/Simulink, the performance of the fuzzy PI controller based on the improved PSO is demonstrated to be obviously better than that of the PI controller or the fuzzy PI controller without using the improved PSO under the situation when the wind speed changes suddenly.

An efficient genetic reinforcement learning algorithm for designing fuzzy controllers is proposed. The genetic algorithm (GA) adopted is based upon symbiotic evolution which, when applied to fuzzy controller design, matches well with the local mapping property of a fuzzy rule. Using this symbiotic-evolution-based fuzzy controller (SE-FC) design method, the number of control trials as well as consumed CPU time are reduced considerably as compared to traditional GA-based fuzzy controller design methods and other types of genetic reinforcement learning schemes. The proposed SE-FC design method has been applied to the cart-pole balancing system. Efficiency and superiority of the proposed SE-FC have been verified from this problem and from comparisons with the traditional GA-based fuzzy systems.

Power conditioning system (PCS) is an interface between distributed generation and utility grid. It regulates voltage, current and power transmitted from the hybrid direct fuel-cell/turbine (DFC/T) power plant to utility grid. This paper presents a self-adaptive fuzzy PI controller of three phase inverter in PCS for the DFC/T power plant. One of the main tasks of PCS for distributed generations is power flow control. Traditionally, the control scheme for grid connected inverters is PI controller. However, PI control scheme would lead to large overshoot and long response time when the load increases sharply. Thus, a hybrid fuzzy PI control scheme is proposed in this paper in order to improve the power flow control. The fuzzy controllers can adjust the PI parameters according to the voltage error and the derivative of voltage error. The overall self-adaptive tuning fuzzy PI controller can update the PI parameters in real time, which makes the power flow control much more accurate than conventional PI controllers. Analysis and design methodologies of hybrid fuzzy PI controllers are presented in this paper. The model was developed in Matlab/Simulink environment. Simulation results show that the proposed control scheme can effectively reduce the overshoot and response time compared to the conventional PI controllers.

Manual tuning of Proportional-Integral-Derivative (PID) controller is time consuming, tedious and generally lead to poor performance. PID controller is a simple and intuitive feedback-based control mechanism being useful to track set points and to reject disturbances. This paper presents a computational Intelligence (CI) technique of Whale Optimization Algorithm (WOA) for tuning the PID controller parameters for inverted pendulum. The inverted pendulum is a benchmark problem in control system design because of its high level of instability and non-linearity. It can mimic the behaviour of open-loop unstable systems such as robot manipulator and missile launcher. The metaheuristic algorithm achieved rise time (0.0913), settling time (1.57), maximum overshot (7.9%) and steady-state error (0.0294). Simulation results demonstrated that the WOA-optimized PID controller can provide an improved closed-loop performance over the Ziegler- Nichols tuned PID controller Parameters. The computational intelligence approach also has superior features, such as easy implementation, stable convergence characteristic and good computational efficiency over the conventional methods of Ziegler- Nichols.

A systematic methodology for the design of a learning fuzzy logic control system is presented. The basic design idea is an indirect control approach where selection of control parameters relies on the estimates of process parameters. The control law consists of three components: an online fuzzy identifier, a desired transition model, and a fuzzy controller. The fuzzy version of the signal Hebbian learning law is introduced for adaptively identifying the process relation of the unknown plant. The desired transition model is constructed so that the control designer's goal can be achieved. A computationally efficient way to construct the transition model is provided via a forward-in-time method based on the concept of truncated policy space. Clear trade-offs between control performance and computational complexity are obtained. >