Backlash Nonlinearity Research Articles

Design and Control of a Mechatronic Tracheostomy Tube for Automated Tracheal Suctioning.

Goal: Mechanical ventilation is required to aid patients with breathing difficulty to breathe more comfortably. A tracheostomy tube inserted through an opening in the patient neck into the trachea is connected to a ventilator for suctioning. Currently, nurses spend millions of person-hours yearly to perform this task. To save significant person-hours, an automated mechatronic tracheostomy system is needed. This system allows for relieving nurses and other carers from the millions of person-hours spent yearly on tracheal suctioning. In addition, it will result in huge healthcare cost savings. Methods: We introduce a novel mechatronic tracheostomy system including the development of a long suction catheter, automatic suctioning mechanisms, and relevant control approaches to perform tracheal suctioning automatically. To stop the catheter at a desired position, two approaches are introduced: 1) Based on the known travel length of the catheter tip; 2) Based on a new sensing device integrated at the catheter tip. It is known that backlash nonlinearity between the suction catheter and its conduit as well as in the gear system of the actuator are unavoidable. They cause difficulties to control the exact position of the catheter tip. For the former case, we develop an approximate model of backlash and a direct inverse scheme to enhance the system performances. The scheme does not require any complex inversions of the backlash model and allows easy implementations. For the latter case, a new sensing device integrated into the suction catheter tip is developed and backlash compensation controls are avoided. Results: Automated suctioning validations are successfully carried out on the proposed experimental system. Comparisons and discussions are also introduced. Significance: The results demonstrate a significant contribution and potential benefits to the mechanical ventilation areas.

Robust inverse compensation and control of a class of non‐linear systems with unknown asymmetric backlash non‐linearity

A robust control approach with the inverse backlash compensation is presented for a class of non-linear systems preceded by unknown asymmetric backlash non-linearity. Firstly, the analytical expressions of the inverse compensation error for an asymmetric backlash are obtained by introducing new indicator functions, which make it possible to design a corresponding controller for the asymmetric input backlash. With the developed compensation error expression, conventional robust control approaches can be utilised to deal with such a non-smooth non-linear system. As an illustration, a robust adaptive control strategy is applied to demonstrate the approach. The developed control laws ensure the robust inverse compensation and achieve tracking within a desired accuracy. Finally, simulations performed on an unstable and uncertain non-linear system illustrate and clarify the effectiveness of the developed approach.

Vibration control of a Timoshenko beam system with input backlash

In this study, a novel boundary control algorithm is designed for a class of Timoshenko beams with unknown external disturbance and uncertain input backlash non-linearity. The Timoshenko beam is described by partial differential equations as governing equations and ordinary differential equations as boundary conditions. The representation of input backlash is modified as a desired control input associated with input non-linear error, which will be transformed into the external disturbance. The unknown ‘disturbance-like’ item is defined based on input error and disturbance, and the boundary of this unknown ‘disturbance-like’ item will be estimated by a disturbance observer. The unknown backlash can be handled and the ultimately uniform stability of the closed-loop system is ensured. Numerical simulations are provided to verify the performance of the author's proposed control.

Decentralized Robust Fuzzy Adaptive Control of Humanoid Robot Manipulation With Unknown Actuator Backlash

Due to the fact that backlash nonlinearity is widespread in actuators, it is impossible to ignore its existence and achieve excellent and desirable mechanical system performance. In this paper, the problem of the humanoid robot grasping a common object with unknown actuator backlash is investigated. To tackle the nonsmooth backlash nonlinearity, a smooth adaptive backlash inverse is incorporated to compensate the line-segment effect. Moreover, a decentralized robust fuzzy adaptive control is constructed and developed to guarantee the object's motion and internal forces converge to the predefined values. The stabilities of the signals in the closed-loop system are proven by utilizing the Lyapunov method. In the end, experiments and simulations involving humanoid robot manipulation are conducted to validate the effectiveness of the proposed algorithms.

Dynamic analysis and experimental study of a marine gearbox with crossed beveloid gears

Dynamic modeling of beveloid gears is less developed than that of conventional involute gears with parallel axis because of their complicated mesh mechanism and 3-dimensional dynamic coupling. For evaluating the dynamic characteristics of a marine gearbox with crossed beveloid gears more realistically, a systematic dynamic modeling approach was proposed based on the lumped parameter and the finite element method. Considering the time-varying mesh stiffness excitation, time-varying loaded translational transmission error excitation, sliding friction excitation and backlash nonlinearity, a coupled gear–shaft–bearing–housing dynamic model for a marine gearbox with crossed beveloid gears was developed based on the proposed modeling method. Then, numerical integrations applying the explicit Runge–Kutta formula and the implicit direct integration were used to solve the nonlinear dynamic model. The dynamic transmission error, dynamic mesh force, and dynamic equivalent shaft-bearing supporting force were obtained as well as the dynamic response of the housing. Finally, a test rig was established for the marine gearbox with crossed beveloid gears and vibration tests were performed to investigate the dynamic responses. Through analyzing the responses in time domain and frequency domain, the experimental results compared well with the theoretical dynamic results.

Synthesis of a Hybrid-Observer-Based Active Controller for Compensating Powetrain Backlash Nonlinearity of an Electric Vehicle during Regenerative Braking

Synthesis of a Hybrid-Observer-Based Active Controller for Compensating Powetrain Backlash Nonlinearity of an Electric Vehicle during Regenerative Braking

Backstepping Control for Gear Transmission Servo Systems With Backlash Nonlinearity

The output tracking problem of gear transmission servo (GTS) systems with backlash nonlinearity is studied in this paper. A new concept—“soft degree”—is proposed to overcome the nondifferentiable “hard” characteristic of the backlash nonlinearity. Furthermore, a detailed softening process-static softening is presented, where a backstepping control algorithm is developed to guarantee that the output of the controlled systems can track any given desired sufficiently smooth trajectory by arbitrary precision and the limit cycles that appear due to backlash nonlinearity can be avoided. Simulation results validate the effectiveness of the proposed controller.

A study on load-sharing structure of multi-stage planetary transmission system

Unequal load distribution is a crucial factor in decreasing bearing capacity and stability of the planetary transmission system. In this paper, a dynamical model of two-stage helical planetary gear transmission system is established based on lumped-parameter method and Lagrange general function. Nonlinearity of gear tooth backlash and error is taken into account. Four load-sharing structures are proposed to study the load-sharing performance. A method to calculate dynamic sensitivity of load-sharing coefficient to errors is presented that can provide a reference to component precision determination in order to make planetary system have a better load distribution. Finally, a numerical method of load-sharing performance is validated by a test. These results provide fundamental basis for multi-stage planetary gear transmission system design.

Influence of propeller shaft bending vibration on drivetrain gear dynamics

A new multi-coordinate dynamic model of a hypoid geared rotor system considering the propeller shaft bending effect is formulated. The bending flexibility of propeller shaft is modeled as a lumped parameter set applying the component mode synthesis. The pinion and gear are modeled as flexibly coupled rigid bodies with backlash nonlinearity and time-varying mesh coupling. The kinematic transmission error is assumed to be the main excitation. The solution is obtained by employing the explicit Runge-Kutta integration method with adaptive time step, which yields the dynamic mesh force and also the vibratory response of the gear bodies in time domain. The frequency response functions are then determined by computing the root-mean-square of the time domain solutions at each frequency point. The analyses show that the effect of propeller shaft bending flexibility and damping on the geared rotor system dynamics are found to be mode shape dependent. It is further observed that increasing the damping of propeller shaft can effectively reduce the dynamic mesh force. This indicates that the damping treatment on propeller shaft can be a potential application to reduce the gearbox vibration and noise response.

Robust Adaptive Control for a DC Servomotor with wide Backlash Nonlinearity

In this paper, the problem of driving angular position of a direct current servomotor system with unmodeled wide backlash nonlinearity is addressed. In order to tackle this problem, a control scheme based on an adaptive super twisting algorithm is proposed. In order to implement the proposed controller, information about angular velocity is estimated by means of a robust differentiator. Based on a simplified model of the system, the proposed scheme increases robustness against unmodeled dynamics as backlash, as not all the parameters of the system nor the bounds of the perturbations are required to be known. Experimental results considering a wide backlash angle near to 2π, illustrate the feasibility and performance of the proposed control methodology.

Mode-switching-based active control of a powertrain system with non-linear backlash and flexibility for an electric vehicle during regenerative deceleration

Regenerative braking provided by an electric powertrain is very different from conventional friction braking with respect to the system dynamics. During regenerative decelerations, the powertrain backlash and flexibility excite driveline oscillations, causing the vehicle driveability and the blended brake performance to deteriorate. In this article, system models, including a powertrain model with non-linear backlash and flexibility, and a hydraulic brake system model, are developed. The effects of the powertrain backlash and the flexibility on the vehicle driveability during regenerative deceleration are analysed. To improve the driveability and the blended braking performance of an electric vehicle further, a mode-switching-based active control algorithm with a hierarchical architecture is developed providing compensation for the backlash and the flexibility. The proposed control algorithms are simulated and compared with the baseline strategy under the regeneration braking process. The simulation results show that the vehicle driveability and the blended braking performance can be significantly enhanced by the developed active control algorithm.

Observer-based predictive controller design with network-enhanced time-delay compensation

State feedback control is very attractive due to the precise computation of the gain matrix, but the implementation of a state feedback controller is possible only when all state variables are directly measurable. This condition is almost impossible to accomplish due to the excess number of required sensors or unavailability of states for measurement in most of the practical situations. Hence, the need for an estimator or observer is obvious to estimate all the state variables by observing the input and the output of the controlled system. As such, the goal of this paper is to provide a control design methodology based on a Luenberger observer design that can assure the closed-loop performances of a vehicle drivetrain with backlash, while compensating the network-enhanced time-varying delays. This goal is achieved in a sequential manner: firstly, a piecewise linear model of two inertias drivetrain, which takes into consideration the backlash nonlinearity and the network-enhanced time-varying delay effects is derived; then, a Luenberger observer which estimates the state variables is synthesized and the robust full state-feedback predictive controller based on flexible control Lyapunov functions is designed to explicitly take into account the bounds of the disturbances caused by time-varying delays and to guarantee also the input-to-state stability of the system in a non-conservative way. The full state-feedback predictive control strategy based on the Luenberger observer design was experimentally tested on a vehicle drivetrain emulator controlled through controller area network, with the aim of minimizing the backlash effects while compensating the network-enhanced delays.

An Adaptive Servo Control Strategy for Automotive Electronic Throttle and Experimental Validation

In order to achieve higher precise positioning of the throttle plate, an adaptive servo control strategy is presented for the electronic throttle control system. Compared with the existing results on the electronic throttle control schemes, in this paper, the throttle valve reference tracking controller comprises a proportional-integral-derivative-type feedback controller with adaptive gain parameters, an adaptive feedforward compensator, and adaptive nonlinearity compensators for friction, limp-home (LH), and backlash. The closed-loop controller is realized by only utilizing the information of the throttle valve position measured by a cheap potentiometer of low resolution. The theoretical proof and analysis show that the designed throttle control system can ensure fast and accurate reference tracking of the valve plate angle in the case of the uncertain parameters related to production deviations, variations of external conditions and aging, and the effects of transmission friction, return-spring LH, and gear backlash nonlinearity with uncertain parameters. Moreover, the capability of the adaptive controller to preserve the transient performance and accuracy is evaluated in both simulation and experiment.

A novel framework to design and compare limit cycle minimizing controllers: demonstration with integer and fractional-order controllers

In this paper, a constrained optimization problem is formulated to tune the limit cycle minimizing controllers meeting additional loop-shaping performances such as phase margin and gain crossover frequency. A graphical approach is proposed so as to determine the superior controller in terms of better limit-cycle suppression. The framework is illustrated with a suitable case of elementary servo plant which has separable static backlash nonlinearity in its model. For this plant, integer-order controllers and their fractional counterparts (PI and $$ PI ^\alpha , [ PI ]^\alpha $$ ; PID and $$ PI ^\alpha D^\beta $$ ) are designed and compared. Interestingly, it is found that the fractional controllers produce better limit-cycle responses than their integer counterparts while both meeting the rest of the specifications. Correspondingly, the better sustained oscillations in the plant output response are obtained with fractional controllers. Such a ‘fractional superiority’ is further verified with the closed-loop nonlinear simulation.

Reduced Order Observer Design with DMPC and LQR for System with Backlash Nonlinearity

In this paper, the robust optimal control strategies discrete model predictive control (DMPC) and linear quadratic regulator (LQR) are proposed to solve the problem of backlash nonlinearity present in the two mass system. The DMPC and LQR need information of all the states within the system, so the role of observers become significant, also by doing so the cost on sensors can also be reduced. Here, we have used the full-order observer (FOO) and reduced order observer (ROO) for the state estimation. The FOO estimates all the states within the system, including the measured state, while ROO estimates only those states, those are not measured by the sensors, hence reducing the computations in the closed-loop system. In simulations, the comparisons have been presented between the two control schemes and also between ROO and FOO. From simulations, it is quite clear that the DMPC performance is much better than LQR, while suppressing oscillations due to the presence of backlash in the system. The advantage of using ROO over FOO is that the settling time is reduced, while achieving tracking.

Random dynamics of a nonlinear spur gear pair in probabilistic domain

This paper investigates the response of a spur gear pair subjected to both deterministic and random loads. Backlash nonlinearity and time-varying mesh stiffness in gear systems are considered in the model. Path integration is adopted to capture the random response in probabilistic domain. In the path integration algorithm, the transition probability density function (PDF) within a short time interval is assumed as Gaussian. Then the mean and variance of the responses are calculated and expressed as closed forms for two different cases in gear systems, which are further used to construct the transition PDF. The simulation results are compared with that from Monte Carlo (MC) simulation and deterministic numerical integration. Good agreements are shown between these results. In addition, the multi-solutions feature characterizing the nonlinear gear system is also captured.

Research on Backlash Nonlinearity in AC Servo-driven Precision Transmission System

AC servo-driven precision transmission system is mainly composed of AC servo motor, mechanical transmission parts and control parts. Because of mutual coupling between various parts, particularly transmission system in mechanical coupling vibration in non-smooth transition, it will be of great harm to safe operation of the system. This paper made some overview and built the model of AC servo-driven precision transmission system mainly from the perspective of backlash nonlinear characteristic and with simulation tool of Matlab/Simulink to analyze the influence of backlash on the precision of servo system, and then corresponding simulation curve and conclusions were shown in this paper. Do hope the work above will have certain reference significance to actual engineering application. DOI : http://dx.doi.org/10.11591/telkomnika.v12i6.5394 Full Text: PDF

Robust Switching Control Strategy for a Transmission System with Unknown Backlash

This paper proposes a robust switching control strategy for a transmission system with unknown backlash. Firstly, the adverse effects of backlash nonlinearity in the transmission system are analyzed. Then the backlash model and different operating modes of the transmission system with backlash are investigated. For each operating mode, an individual controller is designed to make the system robust against the unknown backlash and various frequencies of the input signal. Moreover, a supervisory controller is proposed to estimate the current mode of the transmission system and coordinate the controller switching between different modes. Simulations are done to verify that our switching control strategy can efficiently reduce the oscillation caused by backlash and is quite robust against the variation of the frequency of the input signal.

Fuzzy neural control of uncertain chaotic systems with backlash nonlinearity

In this paper, a class of uncertain chaotic systems preceded by unknown backlash nonlinearity is investigated. Combining backstepping technique with fuzzy neural network identifying, an adaptive backstepping fuzzy neural controller (ABFNC) for uncertain chaotic systems with unknown backlash is proposed. The proposed ABFNC system is comprised of a fuzzy neural network identifier (FNNI) and a robust controller. The FNNI is the principal controller utilized for online estimation of the unknown nonlinear function. The robust controller is used to attenuate the effects of the approximation error so that the stability and control performance of the closed-loop adaptive system is achieved always. Finally, simulation results show that the ABFNC can achieve favorable tracking performances.

Adaptive inverse control for parametric strict feedback systems with unknown failures of hysteretic actuators

SummaryAn adaptive compensation control scheme is proposed by using backstepping techniques for a class of uncertain nonlinear systems preceded by m hysteretic actuators, which exhibit unknown backlash nonlinearity and possibly experience unknown failures. An estimated smooth inverse of the actuator backlash is utilized in the controller design to compensate for the effects of the backlash and actuator failures. It is shown that the designed controllers can ensure all signals of closed‐loop system bounded for any failure pattern of hysteretic actuators and tracking performance is also maintained. Simulation studies confirm the effectiveness of the proposed controller, especially the improvement of system performances. Copyright © 2013 John Wiley & Sons, Ltd.