This article proposes an unknown system dynamics estimator (USDE) based sliding mode control for servo mechanisms with unknown dynamics and modeling uncertainties. An invariant manifold is first constructed by introducing an auxiliary variable based on a first-order low-pass filter. This is used to design a USDE with only one tuning parameter (i.e., time constant for the filter) and a simpler structure than other estimators. The USDE is used to compensate for the effect of the lumped unknown system dynamics since it can be easily incorporated into control synthesis. Moreover, to avoid the chattering phenomenon in the conventional sliding mode control methods, a novel reaching law is designed based on hyperbolic functions to guarantee that the sliding mode variable infinitely approaches to the equilibrium point instead of crossing it. Consequently, the fast convergence and chattering-free property can be achieved simultaneously. Simulations and experiments are provided to validate the effectiveness and superior performance of the proposed method.

USDE-Based Sliding Mode Control for Servo Mechanisms With Unknown System Dynamics

Speed loop is the key factor affecting the performance of induction machine (IM) drives. Conventionally, the proportional integral (PI) controller is applied for its simple implementation and static-errorless; however, its performance degrades apparently under sudden external load torque changes. To address this problem, this paper presents a nonlinear control strategy, combining the conventional PI control with a high-order fast terminal sliding-mode (HOFTSM) load torque observer. The external load torque is estimated online by the proposed HOFTSM observer, and then the estimated torque is used as feed-forward compensation for the PI controller. Moreover, the designed HOFTSM observer shows superiorities in fast convergence rate and chattering elimination. Comparison experiments show that the load torque rejection of the IM speed loop is significantly enhanced by using the proposed approach.

Antidisturbance Speed Control for Induction Machine Drives Using High-Order Fast Terminal Sliding-Mode Load Torque Observer

In this paper, a predefined time sliding mode control with prescribed performance is presented for dual-inertia driving systems with unknown disturbances. A modified prescribed performance function (PPF) without requiring the accurate initial error is designed to guarantee that the tracking error remains within the prescribed boundary. An adaptive law is then constructed to estimate the unknown upper boundary parameters of the lumped dynamics (e.g., parameter uncertainties and external disturbances), so that the prior knowledge of the upper bound of uncertainties is not required. The parameter estimation is incorporated into the control design to eliminate the effects of the unknown dynamics. Using the sliding mode technique, an adaptive predefined time sliding mode control is developed. The proposed control method can achieve fast convergence rate of the tracking error, and the stability of the closed-loop system is proved via the Lyapunov function method. Comparative experiments are carried out based on a dual-inertia driving system to validate the efficacy of the proposed approach.

Adaptive Predefined Performance Sliding Mode Control of Motor Driving Systems With Disturbances

Mechanical resonance is a common problem in drive systems with elastic coupling. On-line adaptive notch filter is widely used to make systems stable and the key of this method is to identify natural torsional frequency from a speed feedback signal. However, because of common adoption of digital control and expansion of system bandwidth, oscillation frequency of the system is more likely to deviate from natural torsional frequency to a higher one. When oscillation frequency is shifted, the enabled notch filter with erroneous notch frequency causes an oscillation with a lower frequency and even makes resonance more severe. In order to explain this phenomenon, the classical two-mass model based classification of resonances is checked at first. Then, by taking digital control, current loop delay, and saturation nonlinearity into consideration, an improved digital mechanical resonance model is proposed and a criterion for oscillation frequency deviation is finally obtained. Furthermore, a more widely applicable and robust notch filter tuning strategy with no oscillation rebound is presented. In the end, the validity of aforementioned analysis and strategy is verified by experimental results.

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Analysis of Oscillation Frequency Deviation in Elastic Coupling Digital Drive System and Robust Notch Filter Strategy

This paper aims to present a solution for torsional vibration suppression and shaft torque limitation simultaneously in servo system with backlash The existence of backlash, which would make conventional notch filter invalid, will aggravate the mechanical vibration and bring the risk of unsafety to the system In order to solve that problem, a novel shaft torque compensator is proposed, which would make the system similar to a rigid system with one inertia What is more, this compensator can limit shaft torque as expected, making the system relatively safe under any situation with different load inertias and torques The limiting control is based on the adaptive online identification of load inertia in order to improve robustness of the system and ensure not only the accuracy, but also the arbitrariness of shaft torque limit Simulation and experimental results are presented to illustrate the favorable behavior of the drive with the robust shaft torque compensator

Shaft Torque Limiting Control Using Shaft Torque Compensator for Two-Inertia Elastic System With Backlash

In this paper, the application of model predictive control (MPC) for torsional vibration suppression and shaft torque limitation control in the elastic drive system is demonstrated Standard MPC is converted to fast explicit MPC (EMPC) to solve its difficult online implementation issues Constraint condition of shaft torque limitation control is first proposed through theoretical derivation, implying that the responses of shaft torque vary with the changed critical value of shaft torque, but the limitation function can still be available Eventually, the EMPC-PI switching control is used for the application of shaft torque limitation control into the typical drive successfully, which can significantly reduce the amount of data storage, closer to practical industrial applications Meanwhile, the advantage of eliminating the steady-state error provided from the PI controller can further enhance robustness of the system, compared with the pure EMPC controller The switching criterion is based on the speed hysteresis value, which can be properly adjusted under different circumstances Simulation and experimental results of speed step responses verify the EMPC-PI switching controller as a more effective approach compared with the PI controller designed by pole-placement method

Vibration Suppression With Shaft Torque Limitation Using Explicit MPC-PI Switching Control in Elastic Drive Systems

This paper mainly deals with the prediction and suppression of limit cycle oscillation existed in the two-mass system with nonlinear backlash. To improve position control precision of the drive system, the full-closed-loop feedback scheme is considered. Then, a comprehensive and definite prediction of limit cycle is given via the describing function method. In order to compensate backlash nonlinearity, the state feedback control method is employed. To overcome the insufficient application of the state feedback control in the complex nonlinear system, a novel design concept is proposed. The influence of backlash on the nonlinear system is substituted with an additional compensation component to the control signal, making the system approach a linear one. Following this, a pole placement scheme is designed, which aims to establish a feedback structure that can make the system equivalent to a rigid system. In such a case, the limit cycle oscillation can be eliminated; thus, the position control precision can also be enhanced. In all cases, the validity of the proposal is verified by experimental results.

Analysis and Suppression of Limit Cycle Oscillation for Transmission System With Backlash Nonlinearity

In servo system, elastic component in transmission can produce mechanical resonance The existence of backlash will aggravate the damage of resonance According to dead-zone model, two-mass elastic system with backlash is established The conclusion that the existence of backlash decreases the elastic coefficient of shaft equivalently and its quantitative relation are researched This paper proposes a torque disturbance observer to realize the suppression of mechanical resonance with limiting control for shaft torque amplitude The observer can decrease ratio of inertia equivalently in the case of no identification of backlash value It has a compensation result that system is changed to a rigid system with single moment of inertia In addition, this compensation algorithm is independent with parameters and configuration of speed controller Simulations and experiments demonstrate the effectiveness of this torque disturbance observer

Suppression of mechanical resonance using torque disturbance observer for two-inertia system with backlash

The main objective of this paper is to focus on the study of limit cycle characteristics due to backlash nonlinearity in drive system. For a two-mass system, the existence of gear reduction mechanism or ball screw will introduce transmission backlash inevitably, which can aggravate mechanical resonance. Therefore, it is essential to study the limit cycle characteristics, so as to provide a good theoretical basis for limit cycle suppression. Firstly, based on describing function analysis, the system is separated into linear part and nonlinear part in order to facilitate the analysis. Then the stability and oscillation frequency of limit cycle are predicted. Through the study, it is found that the increasing of backlash amplitude does not affect the limit cycle frequency, yet it will aggravate the oscillation amplitude. Moreover, the limit cycle frequency and amplitude will increase with the increasing of system control stiffness. Finally, the theoretical analyses are confirmed by the experimental results.

Weilong Zheng

Papers

Vibration Suppression With Shaft Torque Limitation Using Explicit MPC-PI Switching Control in Elastic Drive Systems

Shaft Torque Limiting Control Using Shaft Torque Compensator for Two-Inertia Elastic System With Backlash

Analysis and Suppression of Limit Cycle Oscillation for Transmission System With Backlash Nonlinearity

Suppression of mechanical resonance using torque disturbance observer for two-inertia system with backlash

Analysis of limit cycle mechanism for two-mass system with backlash nonlinearity