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# Integrated measurement method of LuGre model for servo turntable

### Date:2017-05-10 Author: Click:

Inverter turntable LuGre model friction parameters and the moment of inertia of the integrated measurement method: to obtain the turntable drive motor input equivalent capacitance C, inductance L, input resistance R, motor back EMF Kb, torque coefficient Cm; control turntable to do uniform rotation, The angular velocity and current curve of the turntable are obtained by measuring the angular velocity of the turntable MC and the viscous friction coefficient σ2. The angular velocity variation curve ω0 (t) of the free-deceleration process under the friction is measured. The dynamic parameters of the LuGre model (Ωs, Ms, σ0, σ1, J], t). The evaluation criterion is set by using the optimization algorithm to make ω ([ωs, Ms, σ0, σ1, J], t) approximates ω0 (t) to identify the input parameters of the fitting curve.

The integrated measurement method of friction parameters and moment of inertia of the servo turntable LuGre model is characterized by the following steps:

(1) to obtain the turntable drive motor input equivalent capacitance C, inductance L, input resistance R, motor back EMF Kb and torque coefficient Cm;

(2) control the turntable to do constant rotation, measuring the turntable angular velocity, current curve, according to the motor torque balance formula Cm ia = MC + σ2 · ω obtained Coulomb moment Mc and viscous friction coefficient σ2, where ia for turntable Drive the armature current of the motor, ω is the angular velocity of the turntable drive motor;

(3) measuring the turntable drive motor input open circuit, only the friction under the free deceleration process of the angular velocity curve where ts is the angular velocity attenuation to 0 adjustment time;

(4) Based on the dynamic parameters of the LuGre model, the angular velocity ωs, the maximum static friction force Ms, the mane stiffness σ0, the microscopic damping coefficient σ1 and the turntable moment of inertia J are the input variables, and the time t is the independent variable. The method is as follows: (a) Using the motor armature circuit voltage balance equation: The armature current of the turntable drive motor is obtained by the continuous system discretization method ia Recursive formula: ia (k) = b1 · i (k-1) + ... + (K) = b1 · i (k-1) + ... + bn · i (kn) + a1 · () () () () () () () () Ω (k-1), ω (k-2), ..., ω (km)} is a discrete expression input signal sequence, M is the highest order order of the input signal in the discrete expression, {ia (k), ..., ia (kn)} is the output signal sequence, n is the highest order of the output signal, b1, ..., bn , A1, ..., am for each order coefficient; (c) using LuGre model expression.

This kind of servo turntable measurement method does not need to install the torque sensor, does not destroy the integrity of the turntable; in the measurement process only need to drive current, turntable angular velocity and other information, to achieve convenient, and can accurately describe the friction process complex dynamic, static characteristics , To facilitate the turntable for high-precision control.