H∞ adaptive fuzzy control technique for high performance drives: practical implementation

In this paper, we consider the design of adaptive iterative learning control for a class of uncertain nonlinear discrete-time systems with unknown control direction. A new design methodology using two fuzzy systems is presented to deal with the problem of unknown sign and upper bound of the input gain function. The fuzzy systems are used as approximators to compensate for the system unknown nonlinearities. In order to solve the uncertainties from fuzzy approximation errors and random input disturbance, a dead zone like auxiliary error with a time-varying boundary layer is introduced. The auxiliary error is utilized for the construction of adaptive laws and the time-varying boundary layer is applied as a bounding parameter. Based on a Lyapunov like analysis, we show that the closed-loop is stable and the internal signals are bounded for all the iterations. The learning performance is guaranteed in the sense that the norm of output tracking error vector will asymptotically converge to a residual set which is bounded by the width of boundary layer. Finally, an illustrative example is conducted to verify effectiveness of the proposed fuzzy AILC.

The fuzzy logic system (FLS)-based disturbance accommodation and fuzzy sliding mode control (FSMC) present a new and feasible design algorithm for disturbance accommodation control (DAC) of unknown multi-input-multi-output (MIMO) nonlinear systems in the presence of unmodeled uncertainties, parametric uncertainties, and external disturbances. The disturbance mismatch and the fuzzy approximation error are compensated by FSMC in a sense that the error state trajectory asymptotically converges to zero. The triple fuzzy scheme that unifies the FLS disturbance estimation, the FSMC, and the adaptive fuzzy parameter update laws is proven by Lyapunov-based stability analysis.

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.

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.

Motion control is an essential part of industrial machinery and manufacturing systems. In this article, the adaptive fuzzy controller is proposed for precision trajectory tracking control in biaxial X-Y motion stage system. The theoretical analyses of direct fuzzy control which is insensitive to parameter uncertainties and external load disturbances are derived to demonstrate the feasibility to track the reference trajectories. The Lyapunov stability theorem has been used to testify the asymptotic stability of the whole system, and all the signals are bounded in the closed-loop system. The intelligent position controller combines the merits of the adaptive fuzzy control with robust characteristics and learning ability for periodic command tracking of a servo drive mechanism. The simulation and experimental results on square, triangle, star, and circle reference contours are presented to show that the proposed controller indeed accomplishes the better tracking performances with regard to model uncertainties. It is observed that the convergence of parameters and tracking errors can be faster and smaller compared with the conventional adaptive fuzzy control in terms of average tracking error and tracking error standard deviation.

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 paper, an adaptive fuzzy control scheme for fuzzy systems with multiple delayed state perturbations, time- varying uncertain parameters, and disturbances. These delayed state perturbations, uncertainties, and external disturbances in the fuzzy systems are assumed to be any uncertain bounded but unknown continuous functions. An improved adaptation law with sigma-modification is proposed to estimate such unknown bounds, and on the basis of the updated values of these unknown bounds, a continuous memoryless state feedback controller is constructed for achieving robust stability of the closed-loop system. Based on Lyapunov stability theorem, the proposed adaptive robust fuzzy controller can guarantee that the state converges asymptotically to zero in the presence of multiple delayed state perturbations, time-varying uncertain parameters, and disturbance. In addition, it is also shown that this improved adaptation law with sigma-modification can be applied to the general adaptive control problems to obtain some more exact control results. Finally, an inverted pendulum system is given to demonstrate the validity of the proposed design method.

In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively. The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed. The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances.

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.

In this paper, we propose an adaptive fuzzy output feedback control method for trajectory tracking control problem for robotic systems. Using Lyapunov method, we first develop a stable adaptive fuzzy state feedback control algorithm by assuming that the systems output and its derivatives are available for feedback control design. The algorithm combines fuzzy systems with robust adaptive controller. The fuzzy system approximates the certainty equivalent (CE)-based optimal controller while robustifying adaptive control term is used to cope with uncertainties that appeared from the effect of external disturbance, fuzzy approximation errors and other modeling errors. Then, an output feedback form of the position-velocity (state feedback) controller is proposed where unknown velocity signal is replaced by the output of model-free linear estimator. We show via asymptotic analysis that the tracking performance of the output feedback design can recover the performance achieved under the state feedback control design. Finally, the proposed method is implemented and evaluated on a 2-DOF robotic system to demonstrate the theoretical development for the real-time applications.

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.

Adaptive fuzzy asymptotic tracking control of uncertain nonaffine nonlinear systems with non-symmetric dead-zone nonlinearities

In this paper, we consider the fuzzy controller design problem for output tracking of uncertain strict-feedback nonlinear systems. For comparison, a basic fuzzy control scheme is first constructed based on an existing approach representative in the field. The scheme can effectively reduce the number of parameter estimates, which benefits from the operation of handling the square of the norm of fuzzy weight vector. However, as a tradeoff of such an operation, the asymptotic tracking performance cannot be ensured and the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm transient performance of tracking error cannot be established. To eliminate these performance costs without losing the advantage of the basic fuzzy control scheme, we further propose a performance-oriented fuzzy control scheme. It guarantees that all closed-loop signals are bounded and the tracking error converges to a prescribed interval asymptotically. Moreover, the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm transient performance of tracking error is also established, which explicitly indicates that the transient performance of tracking error can be improved through changing controller design parameters with the performance-oriented fuzzy control scheme. Simulation examples are given to verify the obtained results.

Genetic synthesis of fuzzy logic controllers in turning