Robust adaptive control with disturbance attenuation for nonlinear systems with uncertainty

A nonlinear feedback control design for the adaptive robust H/sub /spl infin// control problem for nonlinear systems with gain bounded uncertainty is presented. An existing control scheme developed for nonlinear systems with relative degree of one is extended to the case where nonlinear systems have general relative degree. A Lyapunov function is constructed that ensures not only the stability of the closed-loop system but also satisfies the dissipation inequality ensuring L/sub 2/-gain performance. Then the controller can be obtained by the recursive use of the existing control scheme. A closed-form solution for the nonlinear H/sub /spl infin// control problem is provided without using a Hamilton-Jacobi inequality in the general relative degree case. Sufficient conditions which nonlinear systems should satisfy for solvability of the problem are provided.

This paper proposes a robust adaptive fuzzy control scheme for the uncertain nonlinear time-delay systems preceded by an unknown dead-zone. It is well known that time-delay and dead-zone characteristics are frequently encountered in various engineering systems. The dead-zone phenomena may occur in various components of control systems including sensors, amplifiers and actuators, especially in pneumatic valves, in electric servo motors and in hydraulic components. On the other hand, the time-delay phenomena are quite commonly found in chemical process, hydraulic systems and pneumatic systems. In most practice motion systems, the dead-zone characteristics are usually poorly known and may vary with time. Therefore, by using a description of a dead-zone and exploring the properties of this dead-zone model intuitively and mathematically, a robust adaptive fuzzy control method is presented without constructing the dead-zone inverse. According to some adaptive laws, the unknown nonlinear functions of the plant are approximated by the fuzzy logic system. Based on Lyapunov stability theorem, the proposed robust adaptive fuzzy control scheme can guarantee the robust stability of the whole closed-loop nonlinear time-delay system with an unknown dead-zone in the actuator and obtain good tracking performance as well. Finally, an example and simulation results are provided to show the efficiency of the proposed control method.

This paper focuses on an adaptive robust dynamic surface control (ARDSC) with composite adaptation laws (CAL) for a class of uncertain nonlinear systems in semi‐strict feedback form. A simple and effective controller has been obtained by introducing dynamic surface control (DSC) technique and designing novel adaptation laws. First, the ‘explosion of terms’ problem caused by backstepping method in the traditional adaptive robust control (ARC) is avoided. Meanwhile, through a new proof philosophy the asymptotical output tracking that the ARC possesses is theoretically preserved. Second, when persistent excitation (PE) condition satisfies, true parameter estimates could be acquired via designing CALs which integrate the information of estimation errors. Finally, simulation results are presented to illustrate the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.

In this article, a robust adaptive self-structuring fuzzy control (RASFC) scheme for the uncertain or ill-defined nonlinear, nonaffine systems is proposed. The RASFC scheme is composed of a robust adaptive controller and a self-structuring fuzzy controller. In the self-structuring fuzzy controller design, a novel self-structuring fuzzy system (SFS) is used to approximate the unknown plant nonlinearity, and the SFS can automatically grow and prune fuzzy rules to realise a compact fuzzy rule base. The robust adaptive controller is designed to achieve an L 2 tracking performance to stabilise the closed-loop system. This L 2 tracking performance can provide a clear expression of tracking error in terms of the sum of lumped uncertainty and external disturbance, which has not been shown in previous works. Finally, five examples are presented to show that the proposed RASFC scheme can achieve favourable tracking performance, yet heavy computational burden is relieved.

In this paper, a novel adaptive robust control (ARC) scheme is proposed for electro-hydraulic servo systems (EHSSs) with uncertainties and disturbances. All dynamic functions in system dynamics are effectively approximated by multi-layer radial basis function neural network (RBF NN)-based approximators with online adaptive mechanisms. Moreover, neural network-based disturbance observers (NN-DOBs) are established to actively estimate and efficiently compensate for the effects of not only the matched/mismatched but also the imperfections of RBF NN-based approximators on the control system. Based on that, the nonlinear robust control law which integrates RBF NNs and NN-DOBs is synthesized via the sliding mode control (SMC) approach to guarantee the high-accuracy position tracking performance of the overall control system. Furthermore, the problem of the combination between DOBs and RBF NNs is first introduced in this paper to treat both disturbances and uncertainties in the EHSS. The stability of the recommended control mechanism is proven by using Lyapunov theory. Finally, numerical simulations with several distinct frequency levels of reference trajectory are conducted to convincingly demonstrate the effectiveness of the proposed approach.

In the paper, based on a combination of the robust control approach and an adaptive control technique, a design procedure of a new robust adaptive controller is proposed for power system load-frequency control with system parametric uncertainties. The system parametric uncertainties are obtained by changing parameters by 30% to 50% simultaneously from their typical values. In the design of the proposed controller, only the bounds of system parameters are required. The motivation of combining the robust control with an adaptive control is to use the robust control approach to deal with the small parametric uncertainties and to use the adaptive control for large parametric uncertainties so that stability of the overall system and good performance can both be achieved for all admissible uncertainties. The simulation results demonstrate that for the example system the proposed load-frequency controller can achieve good performance even in the presence of the generation rate constraint (GRC).

This paper reports a new robust adaptive tracking controller for multi-input/multi-output nonlinear parametric strict-feedback systems in the presence of parametric uncertainty and any unknown continuous bounded additive disturbance. The proposed solution uses a new projection-like adaptation that allows the application of the standard tuning function approach, thereby avoiding over parametrization and the need for extra nonlinear damping-type terms in the control. The robust adaptive control is shown to guarantee practical tracking in the presence of the disturbance and asymptotic tracking when the disturbance disappears.

Utilizing the feature of quick response of HVDC to improve the performance of AC/DC system has become the emphasis to be researched. This paper introduces firstly the principle of the robust adaptive control of nonlinear systems with unmodeled dynamics, then developed the robust adaptive additional control of HVDC with unmodeled dynamics of generator in order to improve stability of power system. The additional control of HVDC with unmodeled dynamics only uses the local signals and its design is simple, furthermore it can obviously improve the stability of power system in different operational conditions. Experimental results using the presented concepts obtained on single machine infinite bus model are also included. These results prove the efficiency of the control scheme. The design process of controller provided a new idea to design controller by use of simplified model.

The problem of adaptive robust control for uncertain nonlinear systems with time-varying delay is considered in this paper. The upper bound of the uncertainty is assumed to be nonlinear functions with unknown coefficients. By using adaptive control method, a class of adaptive robust state feedback controller is proposed. Based on Lyapunov-Krasovskii method and Lyapunov stability theory, it is shown that the controller designed can render the uniform asymptotic stability of the system. Finally, a numerical example is given to show the controller is valid.

To keep the attitude control of maneuvering reentry vehicle in reentry phase, the strict feedback attitude model of reentry vehicle with time-varying parameters is built. An adaptive robust controller is designed based on backstepping, which consists of backstepping adaptive control and robust control. The controller design method uses adaptive strategies to estimate the unknown parameters, introduces robust control to avoid the singularity in parameters estimation of gain matrix phase. Theoretical analysis shows that all signals of the closed-loop system are proved intimately uniform bounded. Simulation results of six-degree-of-freedom demonstrate that the proposed control method has strong robust performance.

This chapter presents a robust Adaptive Fuzzy Neural Controller (AFN C) suitable for identification and control of uncertain Multi-Input-Multi-Output (MIMO) nonlinear systems. The proposed controller has the following salient features: (1) Self-organizing fuzzy neural structure, i.e. fuzzy control rules can be generated or deleted automatically; (2) Online learning ability of uncertain MIMO nonlinear systems; (3) Fast learning speed; (4) Fast convergence of tracking errors; (5) Adaptive control, where structure and parameters of the AFNC can be self-adaptive in the presence of disturbances to maintain high control performance; (6) Robust control, where global stability of the system is established using the Lyapunov approach. Two simulation examples are used to demonstrate excellent performance of the proposed controller.

Adaptive Controller Design for Tracking and Disturbance Attenuation in Parametric-Strict-Feedback Nonlinear Systems

A pneumatic parallel platform driven by an air cylinder and three circumambient pneumatic muscles was considered. Firstly, a mathematical model of the pneumatic servo system was developed for the MIMO nonlinear model-based controller designed. The pneumatic muscles were controlled by three proportional position valves, and the air cylinder was controlled by a proportional pressure valve. As the forward kinematics of this structure had no analytical solution, the control strategy should be designed in joint space. A cross-coupling integral adaptive robust controller (CCIARC) which combined cross-coupling control strategy and traditional adaptive robust control (ARC) theory was developed by back-stepping method to accomplish trajectory tracking control of the parallel platform. The cross-coupling part of the controller stabilized the length error in joint space as well as the synchronization error, and the adaptive robust control part attenuated the adverse effects of modelling error and disturbance. The force character of the pneumatic muscles was difficult to model precisely, so the on-line recursive least square estimation (RLSE) method was employed to modify the model compensation. The projector mapping method was used to condition the RLSE algorithm to bound the parameters estimated. An integral feedback part was added to the traditional robust function to reduce the negative influence of the slow time-varying characteristic of pneumatic muscles and enhance the ability of trajectory tracking. The stability of the controller designed was proved through Laypunov’s theory. Various contrast controllers were designed to testify the newly designed components of the CCIARC. Extensive experiments were conducted to illustrate the performance of the controller.

The problem of adaptive robust control for uncertain systems with multiple time delays is considered. The parameter uncertainties are assumed to be time-varying norm-bounded, whose bounds are unknown. The objective is to design adaptive robust state-feedback controllers such that the resulting closed-loop system is globally uniformly exponentially convergent to a ball with a certain convergence rate. In terms of a linear matrix inequality, a sufficient condition for the solvability of this problem is presented and the expression of a desired adaptive robust state-feedback controller is given. It is shown that the result obtained improves certain existing ones in the literature.

Hydraulic system is widely used in industry where large actuation forces are needed such as electro-hydraulic positioning system, active suspension control, and so on. One of the main problem in hydraulic system is the nontriviality, for instance, the deadbands in valve operation, frictions of links, saturations, pressure dynamics, etc. both system unknown nonlinearities and external disturbances should be considered in controller design. For underwater hydraulic manipulator, because of the environment of sea and the large nonlinearities of the hydraulic manipulator system, both system unknown nonlinearities and external disturbances should be considered in controller design. A lot of control methods have been proposed to solve the problem properly, such as sliding mode control, adaptive control, fuzzy adaptive control, adaptive robust control, ect. However, due to limited knowledge about hydraulic manipulator system, it is hard to precisely estimate the nonlinearities for a possible higher performance. In this paper, a neural network adaptive robust control method is proposed to help control an underwater hydraulic manipulator. In order to achieve better performance using adaptive robust control strategy, unknown nonlinearities in the system are approximated by the outputs of radial basis function neural network (RBFNNs). A projection law has been used to bound the NN weights when they are tuning on-line to avoid possible adaptive divergence, and the tracking transient performance is guaranteed by robust control law. Simulation results illustrate that manipulator has a good tracking performance.