Dead-zone Input Nonlinearity Research Articles

Robust adaptive asymptotic tracking control of a class of nonlinear systems with unknown input dead-zone

This paper considers the tracking control for a class of uncertain single-input and single-output (SISO) nonlinear strict-feedback systems with unknown input dead-zone nonlinearity, parametric uncertainties and unknown bounded disturbances. By constructing a smooth dead-zone inverse and applying the backstepping recursive design technique, a robust adaptive backstepping controller is proposed, in which adaptive control law is synthesized to handle parametric uncertainties and a novel robust control law to attenuate disturbances. The robust control law is developed by integrating a sufficiently smooth positive integral function at each step of the backstepping design procedure. In addition, a smooth projection mapping is used and assumptions are made that the prior knowledge of the extents of parametric uncertainties and the variation ranges of the bounds of disturbances is known to facilitate the backstepping recursive design. However, the exact bounds of disturbances are not required. The major feature of the proposed controller is that it can theoretically guarantee asymptotic output tracking performance, in spite of the presence of unknown input dead-zone nonlinearity, various parametric uncertainties and unknown bounded disturbances via Lyapunov stability analysis. Comparative simulation results are obtained to illustrate the effectiveness of the proposed control strategy.

Boundary control for flexible mechanical systems with input dead-zone

In this paper, the control problem for flexible mechanical systems with input dead-zone nonlinearity is investigated. We employ the boundary control technique aiming at regulating the deformation of flexible mechanical systems (including both the string and the Euler–Bernoulli beam) in the presence of various external disturbances. With the proposed control method, we prove that all the states of the closed-loop flexible mechanical systems are uniformly ultimately bounded, and the input dead-zone nonlinearity and boundary external disturbance are handled. Numerical simulation studies are carried out to verify the effectiveness of the developed boundary control.

Synchronization of Micro-Electro-Mechanical-Systems in Finite Time

Finite time synchronization of chaotic Micro-Electro-Mechanical Sys-tems (MEMS) is considered. In particular, a Lyapunov-based adaptive controller is developed such that convergence of synchronization error is guaranteed globally in the presence unknown perturbations. The system under consideration suffers from bounded parametric uncertainties, additive external disturbances as well as dead zone input nonlinearities. We establish the controller on being resistance against hard nonlinearities by a novel scheme which can be developed to general chaotic systems even. We provide rigorous stability analysis to come up with sufficient conditions that guarantee finite time error convergence of perturbed system. Several simulation scenarios are carried out to verify the effectiveness of obtained theoretical results.

Adaptive robust fuzzy control for dual arm robot with unknown input deadzone nonlinearity

The control problem of the dual arm robot rigidly grasping an object with unknown nonsymmetric deadzone input is investigated in this paper. Due to the factor that the deadzone nonlinearity is widespread in the actuators, a smooth inverse adaptive deadzone is incorporated to minimize the effect of the deadzone nonlinearity in the dual arm robot system to guarantee a high accuracy tracking. Since these type of robots are usually applied in complex environments, a multi-input multi-output fuzzy logic unit is adopted to approximate the manipulator’s dynamics to achieve a accuracy tracking performances. Moreover, a decentralized robust fuzzy adaptive control scheme is constructed to make the motion and internal forces track a reference trajectories in the presence of parameters uncertainty and external disturbance. By using the Lyapunov method, the stability of the signals in the closed-loop system is proved. Simulation result demonstrates that the proposed controller is effective to the dual arm robot system with deadzone nonlinearity.

Robust adaptive neural control of flexible hypersonic flight vehicle with dead-zone input nonlinearity

This paper presents adaptive dynamic surface control for the flexible model of hypersonic flight vehicle in the presence of unknown dynamics and input nonlinearity. By modeling the flexible coupling as disturbance of rigid body, based on the functional decomposition, the dynamics is divided into attitude subsystem and velocity subsystem. Flight path angle, pitch angle, and pitching rate are involved in the attitude subsystem. To eliminate the inherent problem of “explosion of complexity” in back-stepping, the dynamic surface control is investigated to construct the controller. Furthermore, direct neural control with robust design is proposed without estimating the control gain function and in this way the singularity problem could be avoided. In the last step of dynamic surface design, through the use of Nussbaum-type function, stable adaptive control is presented for the unknown dynamics with time- varying control gain function. The uniform ultimate boundedness stability of the closed-loop system is guaranteed. Simulation result shows the feasibility of the proposed method.

Guaranteeing preselected tracking quality for uncertain strict-feedback systems with deadzone input nonlinearity and disturbances via low-complexity control

A continuous, low-complexity, static, state-feedback controller is proposed for strict-feedback systems with deadzone input nonlinearity and disturbances, utilizing the Prescribed Performance Control methodology. The scheme achieves preselected bounds on the transient and steady state output error performance despite the uncertainty in system nonlinearities and deadzone characteristics. Regarding the latter, a general class of admissible deadzones is considered compared to the current state-of-the-art, permitting nonsmooth and even locally decreasing behavior outside the dead-band. Furthermore, approximating structures, i.e., neural networks, fuzzy systems, etc., are not utilized and, moreover, the backstepping “explosion of complexity” issue is eliminated without residing in filtering, thus deriving a low-complexity design. The proposed controller evades the construction of a deadzone inverse and does not employ a special analytical deadzone representation. Simulations are performed to verify the theoretical findings.

Adaptive control of stochastic Hammerstein systems with dead-zone input non-linearity

This article presents a new control scheme for H systems with symmetric dead-zone input non-linearity and coloured noise. Based on the parameterized H model, we derive a dead-zone compensating control law and a recursive estimator. Theoretical analysis shows that global convergence and closed-loop stability can be guaranteed using the proposed algorithms. What is more, theoretical results show that the output tracking error is convergent with a specific residue, which is related to the variance of the noise and the parameter estimate. Simulation results confirm that the proposed method leads to satisfactory output tracking performance.

Recursive identification for Hammerstein–Wiener systems with dead-zone input nonlinearity

A new recursive algorithm is proposed for the identification of a special form of Hammerstein–Wiener system with dead-zone nonlinearity input block. The direct motivation of this work is to implement on-line control strategies on this kind of system to produce adaptive control algorithms. With the parameterization model of the Hammerstein–Wiener system, a special form of model estimation error is defined; and then its approximate formula is given for the following derivation. Based on these, a recursive identification algorithm is established that aims at minimizing the sum of the squared parameter estimation errors. The conditions of uniform convergence are obtained from the property analysis of the proposed algorithm and an adaptive setting method for a weighted factor in the algorithm is given, which enhances the convergence of the proposed algorithm. This algorithm can also be used for the identification of the Hammerstein systems with dead-zone nonlinearity input block. Three simulation examples show the validity of this algorithm.

Output L∞ Neural Dynamic Surface Control for Large Inertia Servo Systems

This paper presents a precise positioning intelligent control scheme for large inertia servo mechanism on the basis of effective compensation of input deadzone nonlinearity. A novel neural observer for estimating system unmeasured states is proposed which is incorporated into dynamic surface control (DSC) algorithm. The output feedback controller and adaptive laws are developed based on Lyapunov stability analysis while Nussbaum function is employed to determine the control direction. L ∞ stability validation guarantees both the transient and steady state performance of overall closed loop system signals. The proposed control scheme is demonstrated numerically by applying it to a second order nonlinear system with unknown input deadzone nonlinearity.

Decentralized sliding mode quantized feedback control for a class of uncertain large-scale systems with dead-zone input

This paper is concerned with the robust quantized feedback stabilization problem for a class of uncertain nonlinear large-scale systems with dead-zone nonlinearity in actuator devices. It is assumed that state signals of each subsystem are quantized and the quantized state signals are transmitted over a digital channel to the controller side. Combined with a proposed discrete on-line adjustment policy of quantization parameters, a decentralized sliding mode quantized feedback control scheme is developed to tackle parameter uncertainties and dead-zone input nonlinearity simultaneously, and ensure that the system trajectory of each subsystem converges to the corresponding desired sliding manifold. Finally, an example is given to verify the validity of the theoretical result.

Robust adaptive control for uncertain nonlinear systems with unknown control directions and actuator nonlinearity

A robust adaptive control scheme is proposed for a class of uncertain nonlinear systems in strict feedback form with both unknown control directions and non-symmetric dead-zone nonlinearity based on backstepping design. The conditions that the dead-zone slopes and the boundaries are equal and symmetric are removed by simplifying nonlinear dead-zone input model, the assumption that the priori knowledge of the control directions to be known is eliminated by utilizing Nussbaum-type gain technique and neural networks (NN) approximation capability. The possible controller singularity problem and the effect of dead-zone input nonlinearity are avoided perfectly by combining integral Lyapunov design with sliding mode control strategy. All the signals in the closed-loop system are guaranteed to be semi-globally uniformly ultimately bounded and the tracking error of the system is proven to be converged to a small neighborhood of the origin. Simulation results demonstrate the effectiveness of the proposed control scheme.

Robust adaptive neural control for a class of uncertain non-linear time-delay systems with unknown dead-zone non-linearity

A robust adaptive neural network controller is proposed for a class of uncertain non-linear time-delay systems in strict feedback form with both completely unknown control gains and unknown non-symmetric dead-zone non-linearity based on backstepping design. The proposed design approach does not require a priori knowledge of the signs of the unknown control gains. The unknown time delays are compensated for constructing appropriate Lyapunov–Krasovskii functionals. By utilising integral Lyapunov design and sliding-mode control strategy, the controller singularity problem and the effect of dead-zone input non-linearity are avoided perfectly. From Lyapunov stability theorem, it is proved that the proposed design approach is able to guarantee semi-globally uniformly ultimately boundedness of all the signals in the closed-loop system, and the tracking error of the system is proven to be converged to a small neighbourhood of the origin. The simulation results demonstrate the effectiveness of the proposed approach.

Simultaneous State and Dead-Zone Parameter Estimation for a Class of Bounded-State Nonlinear Systems

This brief proposes a new estimation technique for nonlinear systems subject to dead-zone input nonlinearities. Using the fact that the dead-zone input nonlinearity can be modeled as a line input function with a bounded disturbance term then, by appropriate selection of a system input, we show that the simultaneous estimation of the dead-zone parameters with the unmeasured system states is possible under some mild conditions. The proposed observation can be applied to both symmetric and non-symmetric dead-zone input with a possible extension to time-varying dead-zone characteristics. To show the usefulness of the developed results, two practical examples including a process system and a dc-motor subject to a nonlinear friction are studied.

Design of uncertain multi-input systems with state delay and input deadzone nonlinearity via sliding mode control

The problem of robust stabilization of a class of uncertain multi-input time-delayed systems with deadzone nonlinearity in the actuator is considered. To achieve a stable uncertain multi-input system, sliding mode control (SMC) is adopted in the controller design. The proposed controller guarantees the global reaching condition of the sliding mode in the uncertain multi-input system. In the sliding mode, the investigated time-delayed systems with deadzone nonlinearity still possess the insensitivity to the uncertainties and/or disturbances, which can be seen in the systems with linear inputs. In addition, the proposed controller can work effectively for systems no matter whether sector nonlinearity and/or deadzone exists in the actuator or not. However, such property cannot be obtained by the controller design through traditional SMC for the systems without input nonlinearity. Besides, the traditional SMC controller might produce limit cycles once the system contains deadzone in the input. Furthermore, the presented controller ensures the system trajectories globally exponentially converged in the sliding mode. Finally, two examples are illustrated to demonstrate the effectiveness of the proposed sliding mode controller.

Anti-synchronization of uncertain unified chaotic systems with dead-zone nonlinearity

This paper addresses chaos anti-synchronization of uncertain unified chaotic systems with dead-zone input nonlinearity. Using the sliding mode control technique and Lyapunov stability theory, a proportional–integral (PI) switching surface is proposed to ensure the stability of the closed-loop error system in sliding mode. Then a sliding mode controller (SMC) is proposed to guarantee the hitting of the switching surface even with uncertainties and the control input containing dead-zone nonlinearity. Some simulation results are included to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.

Variable Structure Output Feedback Control of a Spacecraft Under Input Dead-Zone Non-Linearity

This paper proposes a robust control algorithm for stabilization of a three-axis stabilized flexible spacecraft in the presence of parametric uncertainty, external disturbance, and input dead-zone non-linearity. This control algorithm is based on the variable structure output feedback control (VSOFC) design technique, and explicitly accounts for control input dead-zone non-linearity in the stability analysis. Asymptotically and exponentially stable design methods are investigated for constructing the controller to stabilize the uncertain system. Furthermore, the developed controller is achieved through adaptive VSOFC (AVSOFC) without the limitation of knowing the bounds of uncertainties and perturbations in advance. The AVSOFC law results in substantially simpler stability analysis and improves the overall response. In addition, a modified adaptation control law is presented for the upper bound on the perturbation to improve the adaptive performances such that a new controller is designed that can guarantee the bound of the estimated gains. Numerical simulations show that precise attitude control and vibration suppression can be accomplished using the derived controller for both cases with and without adaptive control.

Generalized projective synchronization of chaotic systems with unknown dead-zone input: Observer-based approach

In this paper we investigate the synchronization problem of drive-response chaotic systems with a scalar coupling signal. By using the scalar transmitted signal from the drive chaotic system, an observer-based response chaotic system with dead-zone nonlinear input is designed. An output feedback control technique is derived to achieve generalized projective synchronization between the drive system and the response system. Furthermore, an adaptive control law is established that guarantees generalized projective synchronization without the knowledge of system nonlinearity, and/or system parameters as well as that of parameters in dead-zone input nonlinearity. Two illustrative examples are given to demonstrate the effectiveness of the proposed synchronization scheme.

Decentralised variable structure control of uncertain large-scale systems containing a dead-zone

In order to deal with dead-zone nonlinearity in the input function through variable structure control theory, a new robust decentralised control scheme is proposed for a class of uncertain large-scale interconnected dynamic systems. Dead-zone characteristics are quite commonly encountered in actuators, such as electric servomotors and electronic circuits. Therefore, in addition to the uncertainties in the system, one must also be concerned with dead-zone nonlinearity in controller design. The proposed variable structure controller ensures the global reaching condition of the sliding mode of the uncertain composite system in the presence of input dead-zone nonlinearity. Also, in the sliding mode, the investigated uncertain composite system remains insensitive to the uncertainties and disturbances, and behaves like a linear system. Furthermore, it is shown that the proposed control law can be applied to uncertain large-scale systems with and without input nonlinearities. Nevertheless, this cannot be guaranteed by the traditional variable structure control design for the systems without dead-zone nonlinearity. Illustrative examples are given to verify the validity of the developed controller.

Global exponential stabilization for a class of uncertain nonlinear systems with time-varying delay arguments and input deadzone nonlinearities

In this paper, the global exponential stabilization for a class of uncertain nonlinear systems with time-varying delay arguments and input deadzone nonlinearities is considered. A composite feedback control is proposed such that the feedback-controlled system is globally exponentially stable if a simple sufficient condition is met. Furthermore, for slightly more restricted systems, we show that the global exponential stability can always be achieved with any pre-specified convergence rate. A numerical example is provided to illustrate the use of our main results.