l2 - 5 5.1 Lab 2 Motor Control Outline This is a two...

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5 Lab 2: Motor Control 5.1 Outline This is a two session experiment which will investigate electric motor control. A schematic diagram of the motor is shown in Figure 1. The applied voltage is denoted by V and is the control input available to us. The outputs of interest are the angular position of the shaft, denoted here by θ , and the angular velocity of the shaft, ˙ θ . + - Vb i + - V RL Load θ Figure 1: Schematic diagram of the motor The motor resistance and inductance are represented by R and L respectively. The back EMF is denoted by V b and is related to the motor speed by, V b = K e ˙ θ, where K e is a motor dependent constant. The output torque of the motor, τ m , is proportional to the motor current, i , τ m = K m i, where K m is another motor dependent constant. For our purposes the load will be approximated by an equivalent torque, τ L , where, τ L = J L ¨ θ + B L ˙ θ. 28

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The load inertia is J L and the viscous damping is B L . A block diagram of the motor model is given in Figure 2. Both θ and ˙ θ are shown as outputs where θ can be derived from ˙ θ in the obvious way. P ( s ) 1 /s ± ± ± ± ± ˙ θ θ V Figure 2: Motor system model. V to θ and ˙ θ On the motors in the lab a tachometer provides a measurement of ˙ θ and a ten turn potentiometer is used to measure the shaft angle. In each case the signals are available to the analog computer as voltages, and in each case there is a constant of proportionality. The complete system, from the voltage input to the two measured voltages is shown in Figure 3. The system shown here, from V to V θ and V ˙ θ , will be denoted by M ( s ). P ( s ) 1 /s K ˙ θ K θ ± ± ± ± ± ± ± V ˙ θ V θ θ ˙ θ V Figure 3: Motor system model, M ( s ). V to V θ and V ˙ θ In the physical system, the motor shaft is connected to the potentiometer by a gear chain. The gear ratios and potentiometer terminal voltages determine the constant K θ . This parameter, and K ˙ θ will be experimentally determined. Several control con±gurations will be attempted for this system. In the ±rst instance we will attempt to control the shaft position by measuring only θ .
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l2 - 5 5.1 Lab 2 Motor Control Outline This is a two...

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