Fuzzy neural networks for direct adaptive control

It is well known that sliding-mode control is simple and insensitive to uncertainties and disturbances. However, control input chattering is the main problem of the classical sliding-mode controller (SMC). In this paper, a fuzzy neural network SMC (FNNSMC) is presented for a class of nonlinear systems. The FNNSMC can eliminate the chattering, unlike the SMC, but there is larger rising time in the FNNSMC than in the SMC. In some cases, small rise time is important. To decrease the rising time of the FNNSMC, an adaptive controller is proposed where the SMC and the FNNSMC are incorporated by a smooth transformation. This adaptive control scheme can improve the dynamical performance and eliminate the high-frequency chattering in the control signal. The system stability is proved by using the Lyapunov function. The simulation results demonstrate the advantages of the proposed adaptive controller.     

Integral sliding-mode control of a magnetically suspended balancebeam: analysis, simulation, and experiment

This paper presents a sliding-mode controller with integral compensation for a magnetic suspension balance beam system. The control scheme comprises an integral controller which is designed for achieving zero steady-state error under step disturbances, and a sliding-mode controller which is designed for enhancing robustness under plant uncertainties. A procedure is developed for determining the coefficients of the switching plane such that the overall closed-loop system has stable eigenvalues. A proper continuous design signal is introduced to overcome the chattering problem. The performance of the balance beam control system is illustrated by simulation and experimental results showing that the proposed integral sliding-mode controller method is effective under external step disturbances and input channel parameter variations     

Use of adaptive fuzzy systems in parameter tuning of sliding-modecontrollers

The paper proposes to combine adaptive fuzzy systems with sliding-mode control (SMC) to solve the chattering problem of SMC for robotic applications. In the design of the controller, special attention is paid to chattering elimination without a degradation of the tracking performance. Furthermore, the a priori knowledge required of the system dynamics for design is kept to a minimum. The paper first considers the basic principles of sliding-mode and fuzzy controllers. Implementation difficulties and most popular solutions are then overviewed. Next, the design of a SMC reported in the literature is outlined and guidelines for the selection of controller parameters for the best tracking performance without chattering are presented. A novel approach based on the introduction of a "chattering variable" is developed. This variable, as a measure of chattering, is used as an input to an adaptive fuzzy system responsible for the minimization. Online tuning of parameters by fuzzy rules is carried out for the SMC. The experimental results obtained are given, and conclusions are presented     

A microcontroller-based induction motor drive system using variablestructure strategy with decoupling

The sliding-mode control concept is applied in the outer loop of a speed drive system utilizing a series-connected wound rotor induction machine (SCWRIM). A design procedure is outlined for the sliding-mode speed controller. The methods of decoupling and torque linearization for the SCWRIM are derived using the field-orientation as well as the torque angle control concepts. Sliding-mode control with cascaded integral operation is used to reduce torque chattering and steady-state error. Accelerator sliding lines are introduced to enable better utilization of the torque capability of the drive system. The parameter-insensitive response provided by this method of control is demonstrated. The effects on the dynamic and static performance with varying drive inertia and load disturbance are studied and compared with the conventional approach using PI control. The influences of sampling effects on sliding-mode control performance are also illustrated and discussed. Microcontroller-based implementation of the speed drive system is employed. Both simulation and experimental results are presented     

Sliding-mode control in voltage source inverter-based higher-order circuits

In this article, a new control methodology of sliding-mode control (SMC) for voltage source inverter (VSI)-based higher-order circuit is proposed. In this method, the SMC is used at the inner terminals for stable tracking of the voltage and current variables. An outer voltage control loop is included to reduce the steady-state error in tracking the reference load voltage. It is shown that when the SMC is applied on the load voltage terminal for higher-order VSI circuits, it leads to the instability. However, it well stabilises the system when the controller is implemented on the inner shunt capacitor terminals. Additional outer voltage control loop with proportional plus integral controller will ensure regulated voltage across the load. It has been shown that the controller is able to achieve good tracking accuracy with an acceptable stability margins. The performance of the proposed SMC has been verified on the fourth-order VSI circuit.     

Fuzzy supervisory sliding-mode and neural-network control for robotic manipulators

Highly nonlinear, highly coupled, and time-varying robotic manipulators suffer from structured and unstructured uncertainties. Sliding-mode control (SMC) is effective in overcoming uncertainties and has a fast transient response, while the control effort is discontinuous and creates chattering. The neural network has an inherent ability to learn and approximate a nonlinear function to arbitrary accuracy, which is used in the controllers to model complex processes and compensate for unstructured uncertainties. However, the unavoidable learning procedure degrades its transient performance in the presence of disturbance. A novel approach is presented to overcome their demerits and take advantage of their attractive features of robust and intelligent control. The proposed control scheme combines the SMC and the neural-network control (NNC) with different weights, which are determined by a fuzzy supervisory controller. This novel scheme is named fuzzy supervisory sliding-mode and neural-network control (FSSNC). The convergence and stability of the proposed control system are proved by using Lyapunov's direct method. Simulations for different situations demonstrate its robustness with satisfactory performance.     

Sliding-mode-controlled slider-crank mechanism with fuzzy neuralnetwork

The dynamic response of a sliding-mode-controlled slider-crank mechanism, which is driven by a permanent-magnet (PM) synchronous servo motor, is studied in this paper. First, a position controller is developed based on the principles of sliding-mode control. Moreover, to relax the requirement of the bound of uncertainties in the design of a sliding-mode controller, a fuzzy neural network (FNN) sliding-mode controller is investigated, in which a FNN is adopted to adjust the control gain in a switching control law on line to satisfy the sliding mode condition. In addition, to guarantee the convergence of tracking error, analytical methods based on a discrete-type Lyapunov function are proposed to determine the varied learning rates of the FNN. Numerical and experimental results show that the dynamic behaviors of the proposed controller-motor-mechanism system are robust with regard to parametric variations and external disturbances. Furthermore, compared with the sliding-mode controller, smaller control effort results and the chattering phenomenon is much reduced by the proposed FNN sliding-mode controller     

一种模糊-PI双模控制系统的仿真与设计

为了提高系统的控制性能,综合了模糊控制和PID控制的优点,提出一种基于模糊-PI双模控制器设计方法。典型的二维模糊控制器因缺少积分环节,难以消除稳态误差,控制的精度常常不能满足系统要求;而PI控制器具有良好的消除稳态误差的作用,所以将其与模糊控制器结合构成复合控制器。通过Matlab/Simulink仿真,结果表明,与经典的PID控制方式相比较,该控制方式在快速性、稳态性及准确性方面都有较大提高。     

Total sliding-mode controller for PM synchronous servo motor driveusing recurrent fuzzy neural network

In this paper, the dynamic responses of a recurrent-fuzzy-neural-network (RFNN) sliding-mode-controlled permanent-magnet (PM) synchronous servo motor are described. First, a newly designed total sliding-mode control system, which is insensitive to uncertainties, including parameter variations and external disturbance in the whole control process, is introduced. The total sliding-mode control comprises the baseline model design and the curbing controller design. In the baseline model design, a computed torque controller is designed to cancel the nonlinearity of the nominal plant. In the curbing controller design, an additional controller is designed using a new sliding surface to ensure the sliding motion through the entire state trajectory. Therefore, in the total sliding-mode control system, the controlled system has a total sliding motion without a reaching phase. Then, to overcome the two main problems with sliding-mode control, i.e., the assumption of known uncertainty bounds and the chattering phenomena in the control effort, an RFNN sliding-mode control system is investigated to control the PM synchronous servo motor. In the RFNN sliding-mode control system, an RFNN bound observer is utilized to adjust the uncertainty bounds in real time. To guarantee the convergence of tracking error, analytical methods based on a discrete-type Lyapunov function are proposed to determine the varied learning rates of the RFNN. Simulated and experimental results due to periodic step and sinusoidal commands show that the dynamic behaviors of the proposed control systems are robust with regard to uncertainties     

A Neuro-Sliding-Mode Control With Adaptive Modeling of Uncertainty for Control of Movement in Paralyzed Limbs Using Functional Electrical Stimulation

During the past several years, several strategies have been proposed for control of joint movement in paraplegic subjects using functional electrical stimulation (FES), but developing a control strategy that provides satisfactory tracking performance, to be robust against time-varying properties of muscle-joint dynamics, day-to-day variations, subject-to-subject variations, muscle fatigue, and external disturbances, and to be easy to apply without any re-identification of plant dynamics during different experiment sessions is still an open problem. In this paper, we propose a novel control methodology that is based on synergistic combination of neural networks with sliding-mode control (SMC) for controlling FES. The main advantage of SMC derives from the property of robustness to system uncertainties and external disturbances. However, the main drawback of the standard sliding modes is mostly related to the so-called chattering caused by the high-frequency control switching. To eliminate the chattering, we couple two neural networks with online learning without any offline training into the SMC. A recurrent neural network is used to model the uncertainties and provide an auxiliary equivalent control to keep the uncertainties to low values, and consequently, to use an SMC with lower switching gain. The second neural network consists of a single neuron and is used as an auxiliary controller. The control law will be switched from the SMC to neural control, when the state trajectory of system enters in some boundary layer around the sliding surface. Extensive simulations and experiments on healthy and paraplegic subjects are provided to demonstrate the robustness, stability, and tracking accuracy of the proposed neuroadaptive SMC. The results show that the neuro-SMC provides accurate tracking control with fast convergence for different reference trajectories and could generate control signals to compensate the muscle fatigue and reject the external disturbance.     

Neural-Network-Based Terminal Sliding-Mode Control of Robotic Manipulators Including Actuator Dynamics

A neural-network-based terminal sliding-mode control (SMC) scheme is proposed for robotic manipulators including actuator dynamics. The proposed terminal SMC (TSMC) alleviates some main drawbacks (such as contradiction between control efforts in the transient and tracking errors in the steady state) in the linear SMC while maintains its robustness to the uncertainties. Moreover, an indirect method is developed to avoid the singularity problem in the initial TSMC. In the proposed control scheme, a radial basis function neural network (NN) is adopted to approximate the nonlinear dynamics of the robotic manipulator. Meanwhile, a robust control term is added to suppress the modeling error and estimate the error of the NN. Finite time convergence and stability of the closed loop system can be guaranteed by Lyapunov theory. Finally, the proposed control scheme is applied to a robotic manipulator. Experimental results confirm the validity of the proposed control scheme by comparing it with other control strategies.      

Accurate Sliding-Mode Control of Pneumatic Systems Using Low-Cost Solenoid Valves

A control law is developed for an inexpensive pneumatic motion control system using four solenoid on/off valves and a position feedback sensor. A sliding-mode approach is used, which is well known for its tolerance for system uncertainties. In contrast to previous control laws, our approach does not use pulsewidth modulation. The control law has an energy-saving mode that saves electrical power, reduces chattering, and prolongs the valve's life. Our simulation and experimental results show that the proposed tracking control law performs very well with good tracking and relatively low steady-state position errors     

Continuous variable structure controller for BLDDSM positioncontrol with prescribed tracking performance

The continuous, accurate, and robust sliding mode tracking controller based on a disturbance observer for a brushless direct drive servo motor (BLDDSM) is presented. Although the conventional sliding mode control (SMC) or variable structure control (VSC) can give the desired tracking performance, there exists an inevitable chattering problem in control which is undesirable for a direct drive system. With the proposed algorithm, not only are the chattering problems removed, but also the prescribed tracking performance can be obtained by using the efficient compensation of the disturbance observer. The design of the sliding mode tracking controller for the prescribed, accurate, and robust tracking performance without the chattering problem is given based on the results of the detailed stability analysis. The usefulness of the proposed algorithm is demonstrated through the computer simulations for a BLDDSM under load variations     

Comparison of sliding-mode and fuzzy neural network control formotor-toggle servomechanism

A comparative study of sliding-mode control and fuzzy neural network (FNN) control on the motor-toggle servomechanism is presented. The toggle mechanism is driven by a permanent-magnet synchronous servomotor. The rod and crank of the toggle mechanism are assumed to be rigid. First, Hamilton's principle and Lagrange multiplier method are applied to formulate the equation of motion. Then, based on the principles of the sliding-mode control, a robust controller is developed to control the position of a slider of the motor-toggle servomechanism. Furthermore, an FNN controller with adaptive learning rates is implemented to control the motor-toggle servomechanism for the comparison of control characteristics. Simulation and experimental results show that both the sliding-mode and FNN controllers provide high-performance dynamic characteristics and are robust with regard to parametric variations and external disturbances. Moreover, the FNN controller can result in small control effort without chattering     

A dead-beat type digital controller for the direct torque control of an induction motor

In this paper, a dead-beat type digital controller has been introduced to overcome the problems of a conventional direct torque controller. The proposed induction motor drive with a digital dead-beat controller shows good transient response and negligible steady-state error even at a low switching frequency, which is needed for high power machines used for transportation. Including the rotor dynamics, the stability condition and steady-state error of the proposed control system have been examined in the z-plane. In addition, the good performance has been verified through the simulation and experiment. The flux and torque controllers have been designed with only stator voltage equations in the stator flux reference frame in order to take advantages of the direct torque control. Therefore, the proposed flux and torque controllers have simple forms and can be easily designed and implemented.     

Neuro sliding mode control of robotic manipulators

In this paper, a synergistic combination of neural networks with sliding mode control (SMC) methodology is proposed. As a result, the chattering is eliminated and error performance of SMC is improved. In the approach, two parallel Neural Networks (NNs) are utilized to realize a neuro-SMC. The equivalent control and the corrective control terms of SMC are the outputs of the NNs. The weight adaptations of NNs are based on the SMC equations in such a way that the use of the gradient descent method minimizes the control activity and the amount of chattering while optimizing the error performance. The approach is almost model-free, requiring a minimal amount of a priori knowledge and robust in the face of parameter changes. Experimental studies carried out on a direct drive arm are presented, indicating that the proposed approach is a good candidate for trajectory control applications.     

Lyapunov-function-based design of fuzzy logic controllers and itsapplication on combining controllers

This paper presents the design of fuzzy logic controllers (FLCs) for nonlinear systems with guaranteed closed-loop stability and its application on combining controllers. The design is based on heuristic fuzzy rules. Although each rule in the FLC refers to a stable closed-loop subsystem, the overall system stability cannot be guaranteed when all these rules are applied together. In this paper, it is proved that if each subsystem is stable in the sense of Lyapunov (ISL) under a common Lyapunov function, the overall system is also stable ISL. Since no fuzzy plant model is involved, the number of subsystems generated is relatively small, and the common Lyapunov function can be found more easily. To probe further, an application of this design approach to an inverted pendulum system that combines a sliding-mode controller (SMC) and a state feedback controller (SFC) is reported. Each rule in this FLC has an SMC or an SFC in the consequent part. The role of the FLC is to schedule the final control under different antecedents. The stability of the whole system is guaranteed by the proposed design approach. More importantly, the controller thus designed can keep the advantages and remove the disadvantages of the two conventional controllers     

Analysis and Experimental Study of Proportional-Integral Sliding Mode Control for DC／DC Converter

DC/DC converter using the proportional-integral (PI) sliding mode control (SMC)scheme is investigated, including the selection of the switching surface, the proof of the reaching condition and the existence condition of sliding motion. The sliding regime and the local stability are given. The implementation of the PI SMC is simpler than other SMC schemes and the steady-state error is eliminated. A prototype based on Buck converter is built up. The experimental results show that the dynamic performance and robustness to the parameter variations and external disturbances are improved.     

基于模糊控制的飞行仿真电动伺服加载系统

飞行模拟器上利用电动伺服加载系统替代传统的电液伺服加载后,需要进一步提高加载系统快速性、扩宽系统频带.建立了电动伺服加载模型,基于不变性原理对多余力矩进行补偿仍不能满足要求的情况下,利用模糊控制的快速响应特性,针对该系统设计出PI和模糊控制相结合的分段复合控制器.通过Matlab仿真结果表明使该系统既保证了控制无静差,静态稳定性好,同时动态性能有了较大提高.     

Application of an auto-tuning neuron to sliding mode control

This paper presents a control strategy that incorporates an auto-tuning neuron into the sliding mode control (SMC) in order to eliminate the high control activity and chattering due to the SMC. The main difference between the auto-tuning neuron and the general one is that a modified hyperbolic tangent function with adjustable parameters is employed. In this proposed control structure, an auto-tuning neuron is then used as the neural controller without any connection weights.. The control law will be switched from the sliding control to the neural control, when the state trajectory of system enters in some boundary layer. In this way, the chattering phenomenon will not occur. The results of numerical simulations are provided to show the control performance of our proposed method.