Dead-zone Operator Research Articles

Model-Based Event-Triggered Tracking Control of Underactuated Surface Vessels With Minimum Learning Parameters.

This article studies the model-based event-triggered control (ETC) for the tracking activity of the underactuated surface vessel (USV). Following this ideology, the continuous acquisition of states is no longer needed, and the communication traffic is reduced in the channel of sensor to controller. The control laws are fabricated in the frame of an adaptive model, which is renewed with the states of the original system whenever the triggering condition is violated. In the scheme, both internal and external uncertainties are approximated by the neural networks (NNs). To decrease the computing complexity, the minimum learning parameters (MLPs) are involved both in the adaptive model and the derived controller. The adaptive laws of only two MLPs are devised, and their updating only happens at triggering instants. Using the MLPs, an adaptive triggering condition is further derived. To avoid the "Zeno" phenomenon in small tracking errors, a dead-zone operator is designed for the triggering condition. Furthermore, we incorporate the dynamic surface control (DSC) into the controller design, such that the jumping of virtual control laws at triggering instants is smoothed and the problem of "complexity explosion" is circumvented. Through the techniques of the impulsive dynamic system and the direct Lyapunov function, the parameter setting for the DSC is derived to guarantee the semiglobal uniformly ultimate boundedness (SGUUB) of all the error signals in the closed-loop system. Finally, the effectiveness of the proposed scheme is validated through the simulation.

Data‐driven‐based event‐triggered tracking control for non‐linear systems with unknown disturbance

A novel event-triggered model-free adaptive tracking control problem is studied for non-linear systems with unknown bounded disturbance. A general dynamic linearisation model framework with disturbance input is developed and event-triggered-based model-free adaptive control algorithm is designed by using pseudo-partial derivatives method and input/output measurement data. Owing to the existence of unknown disturbance, a disturbance estimator is designed based on the optimisation criterion technique. Then, a new event-triggering mechanism with dead-zone operator is designed to improve the utility of network communication resources without Zeno phenomenon. Then, an observer-based controller with disturbance compensation is developed, such that the tracking error between the system output and desired output signal converges to a small residual set around the origin. Finally, two simulation examples are provided to show the effectiveness and practicability of the proposed approach.

Adaptive Neural Event-Triggered Control for Discrete-Time Strict-Feedback Nonlinear Systems.

This paper proposes a novel event-triggered (ET) adaptive neural control scheme for a class of discrete-time nonlinear systems in a strict-feedback form. In the proposed scheme, the ideal control input is derived in a recursive design process, which relies on system states only and is unrelated to virtual control laws. In this case, the high-order neural networks (NNs) are used to approximate the ideal control input (but not the virtual control laws), and then the corresponding adaptive neural controller is developed under the ET mechanism. A modified NN weight updating law, nonperiodically tuned at triggering instants, is designed to guarantee the uniformly ultimate boundedness (UUB) of NN weight estimates for all sampling times. In virtue of the bounded NN weight estimates and a dead-zone operator, the ET condition together with an adaptive ET threshold coefficient is constructed to guarantee the UUB of the closed-loop networked control system through the Lyapunov stability theory, thereby largely easing the network communication load. The proposed ET condition is easy to implement because of the avoidance of: 1) the use of the intermediate ET conditions in the backstepping procedure; 2) the computation of virtual control laws; and 3) the redundant triggering of events when the system states converge to a desired region. The validity of the presented scheme is demonstrated by simulation results.

Modeling and compensation of asymmetric hysteresis for pneumatic artificial muscles with a modified generalized Prandtl–Ishlinskii model

This paper presents a modified generalized Prandtl–Ishlinskii (MGPI) model for the asymmetric hysteresis characterization of pneumatic artificial muscles (PAMs), which can be considered as a cascade of the superposition of weighted generalized play operators and the superposition of weighted dead-zone operators. Compared with the established hysteresis models, the significance of the MGPI model is that it has a simple expression including a small number of parameters to be identified. Besides, the analytical form of its inverse model is easy to be obtained, which can be applied to the compensation of asymmetric hysteresis of the PAM in real-time. The wiping-out and congruency properties of the proposed model are verified by simulations. Meanwhile, by carrying out the experimental study on length–pressure hysteresis of a PAM, the parameters in the MGPI model are identified from measured data using the Levenberg–Marquardt method. Then, a feedforward hysteresis compensator based on the inverse MGPI model is designed for trajectory tracking control of the PAM. The simulation and experimental results indicate that the proposed model and its inversion are effective to characterize and compensate the length–pressure hysteresis of the PAM.

Adaptive Neural Network-Based Event-Triggered Control of Single-Input Single-Output Nonlinear Discrete-Time Systems.

This paper presents a novel adaptive neural network (NN) control of single-input and single-output uncertain nonlinear discrete-time systems under event sampled NN inputs. In this control scheme, the feedback signals are transmitted, and the NN weights are tuned in an aperiodic manner at the event sampled instants. After reviewing the NN approximation property with event sampled inputs, an adaptive state estimator (SE), consisting of linearly parameterized NNs, is utilized to approximate the unknown system dynamics in an event sampled context. The SE is viewed as a model and its approximated dynamics and the state vector, during any two events, are utilized for the event-triggered controller design. An adaptive event-trigger condition is derived by using both the estimated NN weights and a dead-zone operator to determine the event sampling instants. This condition both facilitates the NN approximation and reduces the transmission of feedback signals. The ultimate boundedness of both the NN weight estimation error and the system state vector is demonstrated through the Lyapunov approach. As expected, during an initial online learning phase, events are observed more frequently. Over time with the convergence of the NN weights, the inter-event times increase, thereby lowering the number of triggered events. These claims are illustrated through the simulation results.

An inverse Prandtl–Ishlinskii model based decoupling control methodology for a 3-DOF flexure-based mechanism

A modified Prandtl–Ishlinskii (P–I) hysteresis model is developed to form the feedforward controller for a 3-DOF flexure-based mechanism. To improve the control accuracy of the P–I hysteresis model, a hybrid structure that includes backlash operators, dead-zone operators and a cubic polynomial function is proposed. Both the rate-dependent hysteresis modeling and adaptive dead-zone thresholds selection method are investigated. System identification was used to obtain the parameters of the newly-developed hysteresis model. Closed-loop control was added to reduce the influence from external disturbances such as vibration and noise, leading to a combined feedforward/feedback control strategy. The cross-axis coupling motion of the 3-DOF flexure-based mechanism has been explored using the established controller. Accordingly, a decoupling feedforward/feedback controller is proposed and implemented to compensate the coupled motion of the moving platform. Experimental tests are reported to examine the tracking capability of the whole system and features of the controller. It is demonstrated that the proposed decoupling control methodology can distinctly reduce the coupling motion of the moving platform and thus improve the positioning accuracy and trajectory tracking capability.

Neural Network-Based Event-Triggered State Feedback Control of Nonlinear Continuous-Time Systems

This paper presents a novel approximation-based event-triggered control of multi-input multi-output uncertain nonlinear continuous-time systems in affine form. The controller is approximated using a linearly parameterized neural network (NN) in the context of event-based sampling. After revisiting the NN approximation property in the context of event-based sampling, an event-triggered condition is proposed using the Lyapunov technique to reduce the network resource utilization and to generate the required number of events for the NN approximation. In addition, a novel weight update law for aperiodic tuning of the NN weights at triggered instants is proposed to relax the knowledge of complete system dynamics and to reduce the computation when compared with the traditional NN-based control. Nonetheless, a nonzero positive lower bound for the inter-event times is guaranteed to avoid the accumulation of events or Zeno behavior. For analyzing the stability, the event-triggered system is modeled as a nonlinear impulsive dynamical system and the Lyapunov technique is used to show local ultimate boundedness of all signals. Furthermore, in order to overcome the unnecessary triggered events when the system states are inside the ultimate bound, a dead-zone operator is used to reset the event-trigger errors to zero. Finally, the analytical design is substantiated with numerical results.

Experimental characterization and modeling of stress-dependent hysteresis of a giant magnetostrictive actuator

The hysteresis nonlinearity of giant magnetostrictive actuator (GMA) is stress-dependent. In this paper, laboratory experiments were performed to characterize the stress-dependent hysteresis properties of a GMA under different compressive stresses ranging from −11.3 MPa to −24.3 MPa and harmonic current excitation with amplitudes from 0.6 A to 1.2 A. The experimental results showed that remarkable changes in peak-peak displacement responses, hysteresis loop width and hysteresis loss occurred with the increasing of compressive stress; no significant changes in coercive current were observed. Based on the analysis of experimental data and discussion of the influences of the weights of Modified Prandtl-Ishlinskii (MPI) on the characteristics of hysteresis loops, a stress-dependent Prandtl-Ishlinskii (SDPI) model was proposed by extending the MPI model to describe the effects of compressive stress, in which the weights of deadzone operators are extended as function of compressive stress. Good agreements were obtained between the model simulation results and the experimental data. Additional model validations were given by the performances of tracking control experiments with an inverse feedforward controller. The experimental results have clearly shown that the inverse SDPI is effective for compensating stress-dependent hysteresis including major and minor loops.

Stress-Dependent Hysteresis Modeling and Tracking Control of Giant Magnetostrictive Actuator for Periodic Reference Input

The tracking control accuracy of giant magnetostrictive actuator (GMA) is limited due to its inherent hysteresis nonlinearity. Hysteresis characteristic of GMA is stress-dependent. This paper proposes a stress-dependent Prandtl-Ishlinskii (SDPI) hysteresis model for GMA by extending the modified Prandtl-Ishlinskii (MPI) model to account for the hysteresis of GMA at varying compressive stress. It is shown experimentally that the weights of play operators is non-sensitive to the compressive stress applied in longitudinal direction of GMA and the relationships between weights of deadzone operators and compressive stress could be modeled by quadratic functions. Then the inverse of SDPI model is established and implemented in open-loop feedforward controller for real-time tracking control for periodic reference input. Comparisons are made between feedforward controller with stress-dependent hysteresis model and stress-independent model. Experimental results show that tracking performance is noticeably improved by using SDPI model.

A control study of a kneeless biped locomotion system

In this paper, a control study on a three-degree-of-freedom kneeless biped locomotion system is performed. Based on the biped dynamics and joint trajectories of the walking gait, a robust adaptive control scheme consisting of a control law and an adaptation law was used. The control law has the structure of the inverse dynamics servo but uses estimates of the dynamics parameters in the computation of torques which propel the biped. The adaptation law uses the tracking error to compute the parameter estimates for the control law. To improve the convergence of the estimated parameters, we modify the timing of applying the adaptation by incorporating a dead-zone operation. Our simulation results show that the adaptive control technique can be effectively used for the biped locomotion control. The joint tracking errors can be made acceptably small and the performance is also robust despite relatively large deviations in the initial estimates of the system parameters.