Backlash Nonlinearity Research Articles

An intelligent control method for a flexible-link manipulator with uncertain backlash and model uncertainty

This study examines a new intelligent control method for a single-link flexible manipulator that addresses backlash and model uncertainty. First, a smooth backlash inverse model is constructed to mitigate backlash nonlinearity. Subsequently, a ‘disturbance-like’ term is formulated to recharacterize the coupled term composed of external disturbances and model uncertainty. A new adaptive controller is proposed to compensate for the unknown ‘disturbance-like’ term. Using the proposed control method, the stability of the system is evaluated using the direct Lyapunov theory, ensuring uniform ultimate boundedness. Finally, numerical simulations and experiments are conducted using the Quanser platform. The numerical simulation and experimental results show that the proposed control can ensure a faster convergence rate and effectively reduce actuator input chattering.

Adaptive backstepping sliding mode compensation control for electro‐hydraulic load simulator with backlash links

AbstractWhen a mechanical backlash between the loading piston rod and the steering gear piston rod connection of the electro‐hydraulic load simulator (EHLS), it will lead to poor loading accuracy. To solve this problem, an adaptive backstepping sliding mode controller based on the backlash feedforward compensation and state observer is proposed. First, the mechanism of surplus force generation in the EHLS is analyzed, and a mathematical model containing position disturbance and backlash nonlinearity is established based on the analysis results. Second, a state observer is designed to estimate the system state and the parameter adaptive law is designed to estimate the system parameters. Third, the adaptive backstepping method is combined with the non‐singular terminal sliding mode control (NTSMC) strategy to deal with the position disturbance and parameter uncertainty and to enhance the system's dynamic performance. Finally, a backlash feed‐forward compensator is engineered to restrain the detrimental effects caused by the backlash nonlinearity, and the simulation experimental results show that the designed new method can realize the precise loading of the EHLS under different working conditions, and the surplus force is suppressed better at the same time.

Impact of Backlash Nonlinearity on the Dynamics of Type-3 Turbine-Based Windfarms

Impact of Backlash Nonlinearity on the Dynamics of Type-3 Turbine-Based Windfarms

Grey wolf optimization tuned drivetrain vibration controller with backlash compensation strategy using time-dependent-switched Kalman filter

To improve the performance and durability of vehicle components, efforts have been made to reduce driveline oscillations using advanced active control algorithms. However, existing methods often rely on subjective parameter adjustments, which can be burdensome for designers. This study introduces an effective tuning algorithm for a driveline vibration controller that accounts for nonlinear backlash effects. Initially, a driveline dynamics model is developed to focus on transient oscillations resulting from changes in driving force and the presence of nonlinear backlash. The backlash impact is incorporated into the model through a discontinuous dead-zone region. Two operational dynamics, which are the contact mode and the backlash mode, are considered. A dynamic output feedback [Formula: see text] controller is designed as a baseline controller to mitigate low-frequency resonance in the driveline. A solution for managing the nonlinear backlash challenges is introduced, involving the use of a simple control mode switching algorithm in conjunction with the controller. This algorithm relies on a time-dependent-switched Kalman filter. Additionally, the optimal settings for the parameters needed by the mode-switching algorithm are autonomously determined using the grey wolf optimizer (GWO). The proposed active controller can be implemented in real vehicles by using an on-vehicle acceleration sensor and electronic control unit (ECU). In a simulation environment, the vehicle body vibration is online fed back to the resultant controller, and an actuator is supposed to apply control commands to the driveline. The effectiveness of this newly proposed active controller is confirmed through comparative tests, revealing the superior vibration control.

Robust fuzzy adaptive yaw moment control of humanoid robot with unknown backlash nonlinearity

To achieve an excellent dynamic balance during humanoid robot walks, it is essential to counteract the undesired yaw moment and deal with the nonlinearities existing in the system dynamics. In this paper, the problems of the dynamic balance optimization and yaw moment control for humanoid robot are investigated. First we formulate a constrained dynamic model of compliant joints for robots. Then, a yaw moment control approach based on quadratic objective function is proposed for computing optimal ankle torque to equilibrate the undesired yaw moment. In order to deal with the complicated optimization problem with inequality and equality constraints, a Quadratic Programming (QP) solver based on Linear Variational Inequality (LVI) is adopted. In comparison with the yaw moment control approaches studied previously, the main contributions of this paper are summarized as follows. 1) our newly proposed control scheme is more effective in counteracting the undesired yaw moment for the case of handling object-carrying tasks during walking. 2) a novel adaptive backlash inverse is included in the proposed scheme to cancel the unknown actuator backlash nonlinearity without a prior knowledge of the backlash nonlinearity. By the strict Lyapunov argument, the asymptotic convergence of the system tracking error to arbitrarily small neighborhood of the origin is proved. The simulation examples involving humanoid robot walking are constructed to validate the proposed algorithm.

Deterministic Learning From Adaptive Neural Network Control for a 2-DOF Helicopter System With Unknown Backlash and Model Uncertainty

In this study, we develop a deterministic learning control approach using adaptive neural network (NN) for a two-degrees-of-freedom helicopter nonlinear system subject to unknown backlash and model uncertainty. First, by combining the backstepping and direct Lyapunov approaches, a novel adaptive NN control scheme with an inverse compensation method is proposed to address the input backlash nonlinearity, track specified trajectories, and stabilize the closed-loop system. Simultaneously, uncertain system dynamics are accurately identified and stored as learned knowledge in constant radial basis function NN weights, while satisfying partial persistent excitation. Subsequently, by extracting the learned knowledge, a learning-based controller is constructed to operate the same control tasks to achieve a superior control performance, less backlash nonlinearity, and minimal computational burden. Finally, the validity and efficacy of the proposed scheme are demonstrated through numerical examples and experiments.

Adaptive Neural Network Output-Constraint Control for a Variable-Length Rotary Arm With Input Backlash Nonlinearity.

This article studies the problem of deformation reduction and attitude tracking for a rotated and extended flexible crane arm with input backlash-saturation and output asymmetrical constraint. By employing Halmilton's principle, the arm system model is formulated by a set of partial and ordinary differential equations (ODEs). Given the modeling inaccuracy, a radial neural network (RNN) is used to approximate system parameters. To better design the controllers, the backstepping technique is applied to the control design. For input nonlinearities with backlash and saturation, we reversely transform them as an asymmetric saturation constraint via a virtual input. A barrier Lyapunov function (BLF) containing logarithmic terms is constructed to guarantee the asymmetric output constraints and the uniformly ultimate boundedness and stability of the arm system are proved. Finally, to testify the effectiveness of the proposed controllers, numerical simulations are carried out, and responding simulation diagrams are displayed.

Design of Control Systems with Multiple Backlash Nonlinearities Subject to Inputs Restricted in Magnitude and Slope

Design of Control Systems with Multiple Backlash Nonlinearities Subject to Inputs Restricted in Magnitude and Slope

Nonlinear robust adaptive control for bidirectional stabilization system of all-electric tank with unknown actuator backlash compensation and disturbance estimation

Since backlash nonlinearity is inevitably existing in actuators for bidirectional stabilization system of all-electric tank, it behaves more drastically in high maneuvering environments. In this work, the accurate tracking control for bidirectional stabilization system of moving all-electric tank with actuator backlash and unmodeled disturbance is solved. By utilizing the smooth adaptive backlash inverse model, a nonlinear robust adaptive feedback control scheme is presented. The unknown parameters and unmodelled disturbance are addressed separately through the derived parametric adaptive function and the continuous nonlinear robust term. Because the unknown backlash parameters are updated via adaptive function and the backlash effect can be suppressed successfully by inverse operation, which ensures the system stability. Meanwhile, the system disturbance in the high maneuverable environment can be estimated with the constructed adaptive law online improving the engineering practicality. Finally, Lyapunov-based analysis proves that the developed controller can ensure the tracking error asymptotically converges to zero even with unmodeled disturbance and unknown actuator backlash. Contrast co-simulations and experiments illustrate the advantages of the proposed approach.

Efficient Tuning Scheme of Mode-Switching-Based Powertrain Oscillation Controller Considering Nonlinear Backlash

Efficient Tuning Scheme of Mode-Switching-Based Powertrain Oscillation Controller Considering Nonlinear Backlash

Robust design of vibro-impacting geared systems with uncertain tooth profile modifications via bifurcation tracking

The present work investigates the influence of uncertain tooth profile modifications on the nonlinear dynamic response of a spur gear pair induced by a backlash nonlinearity. To this end, an original approach based on bifurcation tracking is developed. The equations of motion are solved in the frequency domain with the harmonic balance method (HBM) coupled to an arc-length continuation algorithm and a bordering technique. The evolution of the bifurcation points with respect to the uncertain parameter is computed in a deterministic way. The study focuses on minimizing the amplitude-jump instabilities induced by the backlash nonlinearity around the primary resonance peak. The proposed methodology allows for a fast and reliable estimation of the tooth profile modification that minimizes the amplitude-jump instability by defining two criteria using the results of the bifurcation tracking algorithm. Probability density functions (PDF) of various indicators of the severity of vibro-impacts can be computed with Monte-Carlo (MC) simulation with minimal computational burden. Results show that the tooth profile modification that minimizes the amplitude-jump instabilities differs from the optimum obtained with static computations.

Vibro-impact dynamics of large-scale geared systems

This work is concerned with the analysis of vibro-impact responses observed in large-scale nonlinear geared systems. Emphasis is laid on the interactions between the high-frequency internal excitation generated by the meshing process, i.e. the static transmission error and time-varying mesh stiffness, and low-frequency external excitations. To this end, a three-dimensional finite element model of a pump equipped with a reverse spur gear pair (gear ratio \(1\!:\!1\)) is built. The model takes into account the flexibility of the kinematic chain, the bearings and the housing and the gear backlash nonlinearity. A reduced-order model is solved with the Harmonic Balance Method coupled to an arc-length continuation algorithm which allows one to compute the periodic solutions of the system. The onset and disappearance of vibro-impact responses is studied through the computation of grazing bifurcations. Results show that the coupling between the external excitation and the time-varying mesh stiffness term greatly modifies the characteristics of the responses in terms of number and periodicity of impacts and contact loss duration.

Vibration Control for a Nonlinear Three-Dimensional Suspension Cable With Input and Output Constraints

This study is concerned with the dynamical analysis and vibration attenuation for a three-dimensional (3-D) suspension cable system of a helicopter preceded by output constraints and input backlash. First, the dynamic model of a 3-D suspension cable is constructed in accordance with Hamilton’s principle. Then, a backlash inverse compensator is established to tackle the input backlash nonlinearities. Subsequently, three boundary controllers together with output signal barrier functions are proposed to dampen the oscillations while not violating the cable swing constraints. The uniform boundedness of the closed-loop system is guaranteed with recourse to the direct Lyapunov’s method. Finally, the validity and efficiency of the derived control laws are testified through simulation results.

An adaptive backstepping nonsingular fast terminal sliding-mode control for the electromechanical brake system with backlash nonlinearity compensation

With the operation of low-floor trams, unavoidable nonlinear factors such as backlash and parameter perturbation are present in electromechanical brake (EMB) systems. This results in poor clamping force tracking performance and challenges the operational safety of trams. Thus, an adaptive nonsingular fast terminal sliding-mode control algorithm is proposed to address this thorny problem. Firstly, a differentiable function approximates the backlash nonlinearity. Then, a dynamic mathematical model for an EMB system with backlash nonlinearity and parameter perturbation is established. Based on the backstepping control principle, this paper divides the system into three subsystems, and the nonsingular fast terminal sliding-mode control (NFTSMC) algorithm is adopted to design the controller of each subsystem. Notably, the NFTSMC algorithm can solve the parameters perturbation problem by the large switching gains, which may cause the chattering phenomenon. This paper utilizes the adaptive law to establish an adaptive NFTSMC algorithm to improve this phenomenon. Furthermore, the global asymptotic stability of the system is analyzed using Lyapunov theory. Finally, experimental results clearly validate the effectiveness and superiorities of the proposed control algorithm.

Fuzzy Control of Switched Systems With Unknown Backlash and Nonconstant Control Gain: A Parameterized Smooth Inverse

This article addresses fuzzy tracking control question when switched systems are subjected to unknown input backlash, nonconstant control gain, and asymmetric full-state constraints. A new mode-dependent integral barrier Lyapunov function (MIBLF) can handle conservative feasibility conditions that only assure asymmetric full-state constraints and all subsystems share a common controller. To handle unknown input backlash nonlinearities in the presence of unknown nonconstant control gain function, fuzzy logic systems are utilized and a new parameterized smooth backlash inverse (PSBI) is presented. It is hard to construct the barrier Lyapunov function-based controller in the presence of unknown backlash, switching framework, and full-state constraints. By employing the fuzzy logic systems and the PSBI, a novel MIBLF-based adaptive fuzzy controller is presented to overcome this challenge. Furthermore, the presented controller not only prevents violation of all constrained states, but also ensures the boundedness of the closed-loop system. Eventually, feasibility of achieved theoretical results can be proven by two examples.

A Maxwell-Slip Based Hysteresis Model for Nonlinear Stiffness Compliant Actuators

Hysteresis nonlinearity is a common issue in nonlinear stiffness compliant actuators. In this type of actuators, the hysteresis effect is obvious and the associated torque curve is nonlinear. Although many mathematical models have been developed for describing hysteresis, they are usually developed with black-box modeling and the model parameters are difficult to tune to match the experimental data well among inputs with different amplitudes. This article presents a novel hysteresis modeling method for a nonlinear stiffness compliant actuator of which the shapes of the associate torque curves vary with amplitudes. In this method, a concept called “virtual deformation” is adopted to transform the nonlinearity curve into a polyline-based model. Then, a modified Maxwell-slip model is developed to estimate the output torque of the actuator according to the “virtual deformation.” Experiments of the proposed hysteresis modeling method applied in a nonlinear stiffness compliant actuator have been conducted and the results showed that the root-mean-square-error of the estimated torque was reduced by 18.6% and the computation cost was reduced to less than one sixteenth using our proposed hysteresis model compared with nonlinear backlash model.

Dynamic reliability analysis of gear transmission system based on sparse grid numerical integration and saddle‐point approximation method

AbstractGear systems are widely used in various mechanical transmission systems. This paper aims to develop an effective and practical method for dynamic reliability analysis of gear transmission system. The proposed method can comprehensively evaluate the dynamic reliability of gear transmission system by adopting the fourth‐moment SPA method. First, a nonlinear dynamics model of a single‐stage spur gear transmission system is established, which simultaneously takes into account the nonlinear backlash, time‐varying meshing stiffness, and static transmission error. After that, a dynamic reliability model for the tooth surface contact fatigue failure of gear system is established with the uncertainty of the motion, structure, and material parameters using stress‐strength interference (SSI) theory. To be specific, the sparse grid numerical integration (SGNI) method is applied to solve the statistical characteristic parameters of the dynamic reliability of the system. The probability distribution of the performance function is obtained with the fourth‐moment SPA method. Test examples show that the results of the proposed method are consistent with the results obtained by the Monte Carlo simulation (MCS) and superior to the maximum entropy with fractional moments (ME‐FM) method, which verifies the effectiveness of this approach. Finally, the dynamic reliability of the gear transmission system with respect to load times is evaluated.

Vibration Suppression of Electromechanical Actuator Considering Backlash Nonlinearity

As an electromechanical drive system, nonlinear factors are unavoidable in electromechanical actuator (EMA). In this paper, elasticity of shaft and backlash nonlinearity are considered in the model, the effects of elasticity and backlash on EMA are analyzed. In order to suppress the vibration caused by nonlinearity and elasticity, A nonlinear control method based on backstepping method is proposed. The simulation results show that this method can eliminate the limit cycle oscillation (LCO) caused by backlash, and effectively suppress the vibration.

Robust adaptive precision motion control of tank horizontal stabilizer based on unknown actuator backlash compensation

Backlash nonlinearity inevitably exists in the actuator of tank horizontal stabilizer and has adverse effect on the system control performance, however, how to effectively eliminate its effect remains a pending issue. To solve this problem, a robust adaptive precision motion controller is presented in this paper to address uncertainties and unknown actuator backlash of tank horizontal actuator. The controller handles the modeling uncertainties including parameter uncertainties and unmodeled disturbances by integrating adaptive feedforward compensation and continuous nonlinear robust law. Based on the backstepping method, a smooth backlash inverse model is constructed by combining the adaptive idea. Meanwhile, the unknown backlash parameters of the system can be approximated through the parameter adaptation, and the impact of the actuator backlash nonlinearity is effectively compensated via the inverse operation, which can availably improve the tracking performance. Moreover, the adaptive law can update the disturbance ranges of tank horizontal stabilizer online in real time, which enhances the feasibility in practical engineering applications. Furthermore, the stability analysis based on Lyapunov function shows that with the existence of unmodeled disturbances and unknown actuator backlash, the designed controller guarantees excellent asymptotic output tracking performance. Extensive comparative results verify the effectiveness of the proposed control strategy.

Dynamic Analysis of Gear Rattling of a Certain Type of Dual-Clutch Transmission

In order to accurately explore the transmission rattling phenomenon and the influence of different factors on the dynamic characteristics of the gear rattling of the dual-clutch transmission under the condition of preselected gears, this paper establishes the gear rattling dynamics model of the transmission with the 1st gear without preselection and the preselected 4th gear, respectively; The model takes into account factors such as time-varying mesh stiffness, mesh damping, nonlinear oil film force, nonlinear backlash, and the drag torque generated by the clutch in the unengaged state. In addition, the feasibility of the dynamic model was verified by the bench test. On this basis, we took the gear meshing power and system power loss as quantitative indexes to analyze the influence of the preselected gear state and different parameters on the rattle vibration of the transmission. The results show that the pre-selected gear will not have a significant effect on the gears that have been rattled in the non-pre-selected state, and the torque fluctuation of the non-power flow shaft is aggravated by the influence of the transmission power flow branch and transmission ratio at different levels, which makes the overall rattling strength increase. In order to improve the transmission efficiency of the gear, the torque fluctuation of the input end of the system should be reduced as much as possible, and a larger lubricant viscosity can be appropriately selected, the inertia of the empty gear can be properly reduced, and the tooth clearance can be relaxed for selection.