Fuzzy Control of an Uncertain Robot Manipulator with Input Constraint

Adaptive fuzzy dynamic surface control of nonlinear systems with input saturation and time-varying output constraints

Friction and deadzone nonlinearities in the nonlinear dynamic systems act often the main obstacles for higher motion control. It is difficult to achieve effective motion compensation for these types of nonlinearities by traditional linear control methodology without the aid of a proper estimation scheme on nonlinearity. Here, we present an adaptive fuzzy dynamic surface control scheme combined with state and nonlinearity observer and sliding mode control to estimate immeasurable state and compensate undesirable uncertainty on motion control for a strict output feedback nonlinear dynamic system. The adaptive laws of the fuzzy, friction and deadzone observer are derived from the recursive steps of the dynamic surface control. The boundedness and convergence of the closed-loop system are guaranteed by a Lyapunov stability analysis. The performance of the proposed control scheme is verified through simulation and experiment on the robot manipulator.

This paper aims at exploring an adaptive fuzzy dynamic surface control (DSC) with prespecified tracking performance for a class of nonlinear systems in strict‐feedback form. Incorporating DSC technique into fuzzy logic systems (FLSs), it is shown that the design procedure and the computational burden can be greatly reduced. Moreover, by introducing a performance function in controller design, the prespecified tracking performance, i.e. the convergence rate, the allowed maximum overshoot and the steady state error, can be achieved. Simulation results are presented to demonstrate the efficiency of the proposed scheme.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

ABSTRACTIn this paper, a state observer-based adaptive fuzzy dynamic surface control is developed for uncertain discrete-time non-linear pure-feedback multiple-input-multiple-output (MIMO) systems with network-induced time-delay. The uncertainties are approximated by a set of adaptive fuzzy logic systems, with the adjusted parameters updated by a simplified recursive least squares estimation algorithm, combined with a state observer. For a constant known network-induced time-delay, the proposed modified dynamic surface control utilising the predicted system states, expands the acceptable network-induced time-delay and stable operating range for a discrete-time non-linear pure-feedback MIMO system in the network. The simulation results indicate that the presented method is effective.

A robust adaptive neural dynamic surface control (DSC) approach is presented for the longitudinal dynamics of a morphing aircraft in the presence of unknown dynamics and input constraints. For the altitude subsystem, neural systems are utilized to approximate the unknown nonlinear functions with smooth robust compensations to counteract the lumped approximation errors. By combining dynamic surface control and minimal learning parameter techniques, a robust adaptive neural control scheme is proposed and a simple adaptive algorithm is constructed. Meanwhile, an auxiliary system is incorporated into the control scheme to overcome the problem of input saturation. The highlight is that the proposed neural controller not only owns less updated neural parameters, but also has the ability of handling input constraints. It is proved that all the signals in the closed-loop system are bounded. Simulation results demonstrate the effectiveness of the proposed control scheme.

This chapter proposes a new modeling and control scheme for uncertain strict-feedback nonlinear systems based on adaptive fuzzy wavelet network (FWN) and dynamic surface control (DSC) approach. It designs adaptive FWN as a nonlinear-in-parameter approximator to approximate the uncertain dynamics of the system. Then, the proposed control scheme is developed by incorporating the DSC method to the adaptive FWN-based model. Stability analysis of the proposed scheme is provided and adaptive laws are designed to learn all linear and nonlinear parameters of the network. It is proven that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can be made arbitrary small. The proposed scheme does not require any prior knowledge about dynamics of the system and offline learning. Furthermore, it eliminates the “explosion of complexity” problems and develops accurate model of the system and simple controller. Simulation results on the numerical example and permanent magnet synchronous motor are provided to show the effectiveness of the proposed scheme.

Attitude tracking control for variable structure near space vehicles based on switched nonlinear systems

In this paper, a hybrid fuzzy adaptive output feedback control design approach is proposed for a class of multiinput and multioutput strict-feedback nonlinear systems with unknown time-varying delays, unmeasured states, and input saturation. First, fuzzy logic systems are employed to approximate unknown nonlinear functions in the system. Next, a smooth function is used to approximate the input saturation and an adaptive fuzzy state observer is constructed to solve the problem of unmeasured states. Based on the designed adaptive fuzzy state observer, a serial-parallel estimation model is established. By applying adaptive fuzzy dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial-parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws is developed based on Lyapunov-Krasovskii functional. It is proved that all variables of the closed-loop system are bounded and the system outputs can follow the given bounded reference signals as close as possible. A simulation example is provided to further show the effectiveness of this novel control scheme.

This paper is concerned with the problem of adaptive fuzzy dynamic surface control (DSC) for the permanent magnet synchronous motor (PMSM) system with chaotic behavior, disturbance and unknown control gain and parameters. Nussbaum gain is adopted to cope with the situation that the control gain is unknown. And the unknown items can be estimated by fuzzy logic system. The proposed controller guarantees that all the signals in the closed-loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal. Finally, the numerical simulations indicate that the proposed scheme can suppress the chaos of PMSM and show the effectiveness and robustness of the proposed method.

In this paper, an adaptive robust stabilization problem is dealt with for a class of uncertain strict‐feedback nonlinear systems in the presence of unknown structure uncertainties, external disturbances, and unknown time‐varying virtual control coefficients. It is not required to know the upper bounds of external disturbances, as well as the upper and lower bounds of unknown time‐varying virtual control coefficients. The controller is designed by adopting backstepping. In addition, to avoid suffering from the problem of ‘explosion of terms’, a dynamic surface control approach is employed by introducing the first‐order low‐pass filter. Furthermore, at every step of the backstepping design procedure, fuzzy logic systems are used to approximate the unknown structure uncertainties. In particular, the norms of weight matrices and the upper bounds of approximation errors of fuzzy logic systems are supposed to be unknown. It is also shown that the proposed controller can guarantee the uniform boundedness of uncertain strict‐feedback nonlinear systems. Finally, the simulation for a single‐link manipulator actuated by a brush DC motor is carried out to illustrate the validity of the proposed controller.

This paper focuses on the problem of adaptive output-constrained neural tracking control for uncertain nonstrict-feedback systems in the presence of unknown symmetric output dead zone and input saturation. A Nussbaum-type function-based dead-zone model is introduced such that the dynamic surface control approach can be used for controller design. The variable separation technique is employed to decompose the unknown function of entire states in each subsystem into a series of smooth functions. Radial basis function neural networks are utilized to approximate the unknown black-box functions derived from Young's inequality. With the help of auxiliary first-order filters, the dimensions of neural network input are reduced in each recursive design. A main advantage of the proposed method is that for an -order nonlinear system, only one adaptation parameter needs to be tuned online. It is rigorously shown that the proposed output-constrained controller guarantees that all the closed-loop signals are semiglobal uniformly ultimately bounded and the tracking error never violates the output constraint.

A composite learning dynamic surface control is proposed for a class of multi-machine power systems with uncertainties and external disturbances by using fuzzy logic systems (FLSs) and disturbance observer (DOB). The main characteristics of the proposed strategy are as follows: (1) The approximation ability of FLSs for nonlinear model of multi-machine power systems is enhanced considerably by using the composite learning method and providing additional correction information for the FLSs. These findings differ considerably from previous designs that focus directly on the system's tracking performance. (2) The filtering errors caused by the utilizations of the first-order low-pass filters in dynamic surface control (DSC) are compensated effectively by designing the compensating signals in the control law design process. (3) The compound disturbances including the FLSs' approximation error and external disturbances are estimated and mitigated by constructing DOB. Finally, the proposed control algorithm is verified on the StarSim Hardware-in-loop experimental platform, and the experimental results validate the effectiveness of the proposed control strategy in suppressing disturbances and enhancing the robustness of the controller.

The paper presents a global tracking fuzzy control design for strict feedback systems with unknown control affine nonlinearities. In particular, the so-called explosion of complexity problem alleviated via using a modified dynamic surface control (DSC) technique. The modification mainly involves a firstorder filter with a space-modulated input, which in turn ensures the boundedness of the filter states. However, the repeated differentiations in the auxiliary robust controller remains as the price of preserving the global stability. Nevertheless, since the adaptive fuzzy controller dominates most of the time, the overall controller still significantly improves the existing global designs in terms of computation and implementation. Simulation results are provided to demonstrate the validity of the proposed scheme.

In this paper, a dynamic surface control (DSC) based adaptive fuzzy backstepping method is proposed for AUV (autonomous underwater vehicle) systems. The DSC is utilized to solve the “explosion of complexity” of traditional backstepping, the fuzzy logic systems(FLSs) are used to approximate unknown nonlinear function of AUV systems and the adaptive backstepping is employed to design controllers, and Matlab is used to conduct the simulation. The proposed control method can achieve position tracking effectively. The simulation results show that the adaptive fuzzy controller can overcome the influences of parameter uncertainties and load disturbance as well as achieve a good control effect on AUV system. This study has lots of practical application value.

This paper addresses the adaptive neural network tracking control problem for a class of strict-feedback systems with unknown non-linearly parameterised and time-varying disturbed function of known periods. Radial basis function neural network and Fourier series expansion are combined into a new function approximator to model each suitable disturbed function in systems. Dynamic surface control approach is used to solve the problem of ‘explosion of complexity’ in backstepping design procedure. The uniform boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to a small residual set around the origin. A simulation example is provided to illustrate the effectiveness of the control scheme designed.