DC MOTOR FUZZY MODEL BASED OPTIMAL CONTROLLER

Bellman’s discrete dynamic programming is one of the most general approaches to solve optimal control problems. For discrete-time dynamical systems, it is, at least theoretically, capable to determine globally optimal control laws. In most practical cases, both state and control variables are subject to constraints. Due to the necessity for gridding of the range of both state and control variables in numerical implementations of dynamic programming, the computational effort grows exponentially with increasing system dimensions. This fact is well known as the curse of dimensionality. Furthermore, gridding of intervals representing uncertain system parameters is inevitable, if dynamic programming is used for the design of optimal controllers for systems with uncertainties. In this contribution, an interval arithmetic procedure for the design of optimal and robust controllers is presented. This procedure relies on the basic concepts of dynamic programming. Sophisticated techniques for the exclusion of non-optimal control strategies significantly reduce the computational burden. Since interval techniques can be applied to both continuous-time and discrete-time dynamical systems, the interval arithmetic optimization approach presented in this chapter is applicable to both cases. In addition, the inclusion of effects of uncertain parameters in the underlying optimality criteria is demonstrated. For that purpose, interval arithmetic routines for analysis and design of optimal and robust controllers have been developed. Details about computationally efficient implementations of interval arithmetic optimization procedures and numerical results for a mechanical positioning system with statedependent switchings between different dynamical models for viscous and Coulomb friction are summarized.

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.

The function of the robot is being complex and various. The robot with various inputs generates various outputs. A proper controller is needed to control such a complex robot. We introduce a 2-layer fuzzy controller (2LFC). It can control robustly and has the small number of rules in many input variables. It can not only deal with various inputs but also generate various outputs. The main problem in the fuzzy system is how to design the fuzzy knowledge base. For this specific problem, we optimize the fuzzy controller using the schema co-evolutionary algorithm (SCEA) to find a global optimal solution. Through the design of the optimal fuzzy controller using the SCEA and the simulation of the mobile robot, we verify the efficacy of the 2-layer fuzzy controller and the schema co-evolutionary algorithm.

Summary form only given. This paper presents a computational approach for an offline measurement based design of an optimal damping controller using adaptive critics for a new type of FACTS device - the gate controlled series capacitor (GCSC). Remote measurements are provided to the controller to damp out system modes. The optimal controller is developed based on the heuristic dynamic programming (HDP) approach. Three multi-layer perceptron (MLP) neural networks are used in the design - the identifier/model network to identify the dynamics of the power system; the critic network to evaluate the performance of the damping controller; and the controller network to provide optimal damping. This measurement based technique provides an alternative to the classical linear model based optimal control design. The eigenvalue analysis of the closed loop system is performed with time domain responses using the Prony method. Analysis of the simulation results show potential of the HDP based optimal damping controller on a GCSC for enhancing the stability of the power system.

Type-2 fuzzy model based controller design for neutralization processes

The multiple motor drives are complex and coupled MIMO nonlinear systems. Due to the complexity of their mathematical models the development of effective control systems is quite complicated task. This paper presents the design of optimal control based on the quadratic optimality criterion for the central section of the continuous production line using soft computer methods when fuzzy model of the controlled system has been used. In this case, the proposed method demonstrates non-analytical design of the optimal parameters of PI controller with emphasis on minimal knowledge on the controlled system. The realized experimental measurements on a continuous line laboratory model confirmed the effectiveness and the good dynamic properties of the optimal continuous line controller and also its applicability to others MIMO nonlinear dynamic systems.

Design of an intelligent optimal neural network-based tracking controller for nonholonomic mobile robot systems

This paper presents the design of a robust optimal controller for a five-phase permanent magnet assisted synchronous reluctance motor (PMa-SynRM) used in electric vehicle (EV) application. Conventionally, proportional (P) or proportional-integral (PI) controllers are widely used in the speed control system for traction and industrial applications. Simple structure, low-cost, and ease of implementation are key advantages of these controllers. However, these controllers are not robust enough to cope with large system and converter uncertainties. Furthermore, there is a tight trade-off between the speed and the overshoot of the desired system response. To address these issues, in this study, a robust optimal controller using a dual-loop feedback structure is proposed for multiphase PMa-SynRM. The proposed optimal controller is designed using the linear-quadratic-regulator (LQR) technique. Different practical conditions, including system uncertainties, un-modeled dynamics, and external disturbances, are considered to verify the proposed controller's robustness. Using extensive computer simulations, it is shown that the proposed optimal controller demonstrates higher robustness and design flexibility compared to the conventional controller.

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.

Membership-Function-Dependent Fuzzy Control of Reaction-Diffusion Memristive Neural Networks With a Finite Number of Actuators and Sensors

This chapter investigates the problem of stabilization of nonlinear discrete-time networked control systems (NCS) with event-triggering communication scheme in the presence of signal transmission delay. A Takagi–Sugeno (T–S) fuzzy model and parallel-distributed compensation (PDC) scheme are first employed to design a nonlinear fuzzy event-triggered controller for the stabilization of nonlinear discrete-time NCS. The idea of the event-triggering communication scheme (a soft computation algorithm) under consideration is that the current sensor data is transmitted only when the current sensor data and the previously transmitted one satisfy a certain state-dependent trigger condition. By taking the signal transmission delay into consideration and using delay system approach, a T–S fuzzy delay system model is established to describe the nonlinear discrete-time NCSs with event-triggering communication scheme. Attention is focused on the design of fuzzy event-triggered controller which ensures asymptotic stability of the closed-loop fuzzy systems. Linear matrix inequality- (LMI-) based conditions are formulated for the existence of admissible fuzzy event-triggered controller. If these conditions are feasible, a desired fuzzy event-triggered controller can be readily constructed. A nonlinear mass-spring-damper mechanical system is presented to demonstrate the effectiveness of the proposed method.

This paper presents the stability analysis of fuzzy-model-based control systems. Stepwise membership functions are introduced to facilitate the stability analysis. Through the stepwise membership functions approximating those of the fuzzy model and fuzzy controller, the information of the membership functions can be brought into the stability analysis. Based on the Lyapunov stability theory, stability conditions in terms of linear matrix inequalities are derived in a simple and easy-to-understand manner to guarantee the system stability. The proposed stability analysis approach offers a nice property to include the membership functions of both fuzzy model and fuzzy controller in the LMI-based stability conditions for a dedicated fuzzy-model-based control system. Furthermore, the proposed stability analysis approach can be applied to the fuzzy-model-based control systems of which the membership functions of both fuzzy model and fuzzy controller are not necessarily the same. Greater design flexibility is allowed by choosing the membership functions during the design of fuzzy controllers. By employing membership functions with simple structure, it is possible to lower the structural complexity and the implementation cost. Simulation example is given to illustrate the merits of the proposed approach.

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.

Evolutionary Algorithms for the Design of Optimal Controller - A Review