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WITHDRAWN (7/27/06) Optimal Inertia Ratio Synthesis for a 2-Inertia Servo System by Using Taguchi Method |
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Equipment, Machines & Instruments: Controls |
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In the design of a servo system, the inertia ratio of a motor and a mechanism is one of the important design parameters. In the past, the inertia ratio was set 1:1 to optimize the energy transmission rate from a servomotor to a mechanism. However, we consider that the most important function of a servo system is information transformation from the position (velocity) reference to the position (velocity) response of mechanism. Then in a 2-inertia velocity control system, the criterion to minimize the response error should be selected for a step velocity reference and against disturbance forces. As the minimizing criterion, we applied the Taguchi method with the lower-is-better Signal/Noise ratio of IAE.
The simulated velocity control system was configured by the following dynamical elements: a motor inertia JM, a load inertia JL, a spring Ks, a damper D, a PI controller with a proportional velocity gain Kv and an integral gain Ki, a load inertia compensation gain Kc, back force ratio Kb, a normalized step velocity reference and a normalized torque disturbance. The motor velocity was feedback to PI controller and the velocity of the load was examined.
In applying Taguchi Method, five control factors and these levels were set as follows: JL/JM = (0.25, 0.5, 1.0, 2.0, 4.0, 8.0), Kv = (50, 100, 150), Ks = (50, 100, 150), D = (0, 10, 100) and Kb = (0.6, 0.8, 1.0). The optimal parameters settings by simulations were analyzed to the three conditions: 1) only a step velocity reference was input, 2) only a torque disturbance was input and 3) both the velocity reference and the torque disturbance were input. The simulation led to the optimal parameters for the above three conditions: 1) (JL/JM, Kv, Ks, D, Kb) = (0.5, 150, 150, 100, 1.0), 2) (8.0, 150, 150, 100, 0.6) and 3) (4.0, 150, 150, 100, 1.0). These results show: 1) for the only velocity reference input the smaller inertia ratio was better within the control system was stable, 2) for the only torque disturbance the larger inertia ratio was better and the lower back force ratio, 3) for both the step velocity reference and the torque disturbance the optimal inertia ratio was in middle of the results of 1and 2.
The experimental system was configured by two DC servomotors in which one was the actuator and the other load torque generator, a coupling element and a load inertia disc were attached to the shaft connecting these two motors. In the experiment of the 200 rpm step velocity reference and the step 10% of rated torque disturbance resulted the optimal condition of (JL/JM, Kv, Ks, D, Kb) = (4.0, 150, 150, 100, 1.0). In the experiment The IAE was a half in case of JL/JM = 4.0 and 8.0 compared to JL/JM =1.0 and 0.3, and load torque disturbance rejection ratio was five times larger.
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