When a vehicle is disturbed to have angular motion, sight stabilization system mounted on the vehicle needs to rotate relative to the vehicle in order to stabilize the line of sight. One of difficult problems in such a sight stabilization system is how to deal with friction of bearings especially in slow and small movements, which may cause tracking errors and, hence, deteriorate quality of image obtained by an electro-optical sight. Therefore, precise modeling of the friction mechanism at low velocities would be greatly helpful to enhance the image stabilization.
Various models were suggested in the literature for the friction at low velocities for the control purpose, but their justifications were mostly simulation based. In this paper, a friction model is derived based upon rigorous experiments on a sight stabilization system at low velocities. The model is basically composed of both stiction and slip, but most attentions have been paid to experimentations in the stiction region.
The stiction model was identified based upon a lot of frequency response functions between motor torque and angular amplitude, which were measured by frequency sweeping under the condition where the amplitude of angular vibration as well as static position was kept constant. Experimental results show that the combination of constant stiffness and structural damping is appropriate for the stiction force modeling at a given response command for the angular amplitude and that these parameters decrease with increase of the response command. Since, however, control of the friction by implementing into the control algorithm is the final goal in our study, the structural damping was replaced with a viscous damping and a lag compensator so that the model might be manipulated in time domain for the control. In the slip region, Coulomb friction force was obtained by observing the angular displacement as well as angular velocity while the motor torque was increased slowly in the open loop control.
Friction characteristics were investigated with temperature change in the stiction region because they are sensitive to temperature. Considering the operational temperature of the sight system, the experiment was performed with range from -30℃ to $+60℃. Experimental results show that friction parameters decrease with increase of the response command at a given temperature and they have the small variations between -30℃ and +40℃ at a given amplitude.
To illustrate the usefulness of the suggested friction model the experiments for friction compensation were performed in the position control loop, where the friction compensation controller means the feedforward controller. Also, overcompensation and undercompensation of 20% were performed with respect to the off-line estimated stiffness coefficient while the damping ratio is constant. Experimental results show that friction compensation improves the tracking performance and the variation of friction parameters is not sensitive to induce the unstable system.
Finally, the low velocity tracking and stabilization performances of a sight stabilization system are analyzed by using the suggested friction model and the effects of friction are discussed. Also, the friction compensation method is suggested to improve the control performances in velocity control loop with gyro.