Optimal design of a 2-layer fuzzy controller using the schema co-evolutionary algorithm

A novel design technique for high performance drives employing both H/spl infin/ optimal control and fuzzy control is proposed in this paper. The fuzzy control design is equipped with an adaptive learning algorithm to achieve H/spl infin/ tracking performance with external disturbances. It gives elevation to the selection of optimal performance weights without any trial and error attempt. The idea is to establish a link between H/spl infin/ optimal control design and fuzzy control design, so as to provide H/spl infin/ tracking design with more intelligence and achieve better performance with fuzzy control design. The effect of both fuzzy logic approximation error and external disturbance on the tracking error is attenuated to an assigned level. The control strategy does not require explicit knowledge of the motor/load dynamics, which is a useful feature when dealing with parameter and load uncertainties. The robustness of the proposed methodology is displayed for different types of trajectories. Experimental and simulation results suggest that the effect of both the fuzzy approximation error and external disturbance on the tracking error can be attenuated efficiently by the H/spl infin/ adaptive fuzzy control. Accordingly, the proposed design method is suitable for the robust tracking control of the uncertain nonlinear drive systems and is an attractive control design philosophy. Test results obtained indicate excellent tracking performance for both speed and position. Test results illustrate the validity of the proposed 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.

We present in this paper a novel method (called PID design through numerical optimization) for the design of adaptive fuzzy PID controllers to achieve optimal control performance. By applying the numerical optimization, the fuzzy PID design problem is transferred to a numerical optimization problem. First, a fuzzy parameter tuner is built to generate initial PID parameters, including positions and shapes of fuzzy membership functions and scaling factors. Then the gradient-based Sequential Quadratic programming (SQP) algorithm is employed to iteratively minimize the cost function by iterating the parameters. Unlike conventional PID design, this method is capable of reaching the desired control performance, such as minimum overshoot or long term stability. Another unique feature is that the optimized adaptive PID controller is applicable to a wide variety of time-varying and nonlinear systems. The proposed method is applied to the induction motor control problem and the experimental results are presented to demonstrate its effectiveness and performance.

Genetic synthesis of fuzzy logic controllers in turning

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.

This paper deals with an optimal design of decoupling-variable structure fuzzy controller for induction motor. It can avoid the randomness of choice of the parameters of a variable structure controller. According to the principle of fuzzy logic control and sliding mode control, the theory of this new fuzzy sliding mode control is presented and a mathematical description for induction motor is given. The sliding mode control is used to achieve robust performance against parameter variations and external disturbances. A fuzzy control law is applied to reduce or overcome the system chattering owing to sliding mode control. The simulant experiment curves and results are given.

This paper presents a comparative study between the firefly algorithm (FA) and the galactic swarm optimization (GSO) method, where the performance of both methods is observed and tested in the optimization of a fuzzy controller for path tracking of an autonomous mobile robot. The main contribution of this work is finding the best method that generates an optimal vector of values for the membership function optimization of the fuzzy controller. This with the goal of improving the performance of the controller and thus the trajectory generated by the autonomous robot is closer to the desired trajectory. It should be noted that the fuzzy controller that is optimized is an interval type-2 fuzzy controller, which has a greater capability for managing uncertainty than a type-1 fuzzy controller. In this case, the limiting membership functions in the interval type-2 fuzzy sets are themselves type-1 fuzzy sets that define the footprint of uncertainty. Type-2 fuzzy controllers have been shown in previous works to handle better the control of robotic systems under noisy and dynamic conditions and this is why their optimal design is very important. Simulation results show that GSO outperforms FA in the optimal design of interval type-2 fuzzy controllers.

Optimal Fuzzy PID Controller Design for Stability of FlexRay Bus in NCS

Optimal fuzzy logic controller design for a plate heat exchanger model

One of the most important considerations in designing any fuzzy controller is the generation of the fuzzy rules as well as the membership functions for each fuzzy set. Metaheuristic algorithms have been widely used for optimal design of fuzzy controllers. In this paper, we propose new auto-tuning fuzzy PD controllers using Tabu Search (TS) for generating knowledge bases for fuzzy logic systems. The algorithm dynamically adjusts the membership functions and fuzzy rules according to different environments. it was tested on the control of angle of inverted pendulum and compared with GA.

This paper presents a new approach towards optimal design of a hybrid fuzzy controller for robotics systems. The salient feature of the proposed approach is that it combines the fuzzy gain scheduling method and a fuzzy proportional-integral-derivative (PID) controller to solve the nonlinear control problem. The resultant fuzzy rule base of the proposed controller can be decomposed into two layers. In the upper layer, the gain scheduling method is incorporated with a Takagi-Sugeno (TS) fuzzy logic controller to linearize the robotics system for a given reference trajectory. In the lower layer, a fuzzy PID controller is derived for all the locally linearized systems by replacing the conventional PI controller by a linear fuzzy logic controller, which has different gains for different linearization conditions. Within the guaranteed stability region, the controller gains can be optimally tuned by genetic algorithms. Simulation studies on a pole balancing robot and a multilink robot manipulator demonstrate the effectiveness and robustness of the proposed approach.

Presents an LMI approach to optimal fuzzy control based on a quadratic performance function. First, stability conditions are presented by relaxing the previous stability results. The relaxed stability conditions are represented in terms of LMIs. The optimal fuzzy controller design utilizing the relaxed stability conditions is proposed. The optimal fuzzy controller is designed by solving the minimization problem that minimizes the upper bound of a given quadratic performance function. Finally, a design example for the well-known nonlinear control benchmark problem, the TORA system, demonstrates the utility of the optimal fuzzy control based on a quadratic performance function.

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.

This paper introduces three hybrid methods for the generation and optimization of rules and membership functions of a fuzzy logic controller for nonlinear systems. The proposed methods overcome the deficiency of a systematic approach for optimal design of fuzzy controllers. An optimally designed fuzzy logic controller should have the least number of fuzzy variables and fuzzy rules and the best possible configuration of fuzzy rules in the rule table. The first strategy of this paper is a two-phase optimization problem: in the first phase, the number of fuzzy variables and their arrangement in the rule table are optimized by a genetic algorithm; in the second phase, the parameters of the membership functions are optimized via extended Kalman filtering. The second strategy tries to achieve the goals of the first method all in one phase by modifying the chromosome structure of the genetic algorithm. Then in the next step, a local search algorithm is utilized to improve the obtained results. The third strategy is similar to the second strategy in structure. However, along with optimizing the number of fuzzy variables and membership parameters, the number of fuzzy rules is also optimized. The first and second strategies are obliged to use every possible combination of fuzzy variables in the rule table; however, the third strategy is capable of distinguishing between useful and useless fuzzy rules in the rule table. The introduced strategies are applied to an automotive cruise control system. The results of the simulations show the effectiveness of the proposed methods and the superiority of the latter approaches over the former ones.

This paper presents a method for the design of optimal fuzzy controller of a DC motor using a fuzzy model based approach with emphasis on minimal knowledge on the controlled system. In the first part of the paper we describe the method of the black-box fuzzy model design based only on the system´s measured input/output data without the necessity of preliminary knowledge of its internal structure and parameters. This fuzzy model is in the second part used in the design of optimal fuzzy controller based on finding the sequence of input signal values that will transfer the controlled system into the desired state in accordance with the selected optimality criterion. The realized simulation and experimental measurements performed on HIL platform have confirmed the correctness and effectiveness of the proposed design method and also its applicability to others dynamic systems with as little previous knowledge as possible.