Question

Mitch is designing a motor driver for a wheeled mobile robot. The motor driver is designed as an inverting amplifier (using the circuit shown in Figure 1) to drive the motor in the opposite direction of the input voltage. Mitch would like to select the components of the amplifier based on specific design requirements. Mitch has installed a switch $(S_w_1)$ to disconnect the motor driver input signal $(v_i_n)$ to the system and a motor protection switch $(S_w_2)$ to disconnect the motor from the amplifier when the motor isn't used. A simplified model of a DC motor has been used, made up of a resistor and inductor in series. The DC motor generates a torque proportional to the current $(i_o_u_t)$ through the inductor.

(a) Design an inverting amplifier by choosing suitable resistor values for $R_1$ and $R_2$ to produce a gain of 5 when both switches $(S_w_1)$ and $(S_w_2)$ are open.

(b) Design the bias input circuit by choosing suitable resistors $R_3$ and $R_4$ such that the voltage $v_b$ will be 2.5V if the positive power supply of the op-amp is connected to a 5V car battery. Again both switches are open.

(c) Given $(S_w_1)$ is open, the amplifier is turned on for enough time, such that the voltages stabilise, Mitch connects the motor by closing $(S_w_2)$ and the motor starts to move. Find the step response of the motor current, $(i_o_u_t)$ . Assume that the amplifier output resistance is negligible, it does not current limit and the motor inductor has been de-energised.

(d) What is the steady state voltage across the motor?

(e) Perform frequency response analysis from $(v_i_n)$ , to the voltage across the motor inductor, when both switches are closed and Mitch applies three different input signals of 10 Hz, 100 Hz and 1000 Hz through the system?

(f) Plot the response calculated in part (e) in a Bode plot.

(g) Mitch has found that the motor input signal has a positive DC offset when it is applied to the motor driver. This DC offset throws off Mitch's original bias circuit that he designed earlier. What single component would be used to remove the effects of this DC offset? Where would this component be placed and why?

Answer 1

Voltage gain of an inverting amplifier when both switches are open is given as 5 - R_2/R_1 = 5 R_2 = 5R_1 for R_1 = 100 ohm implies R_2 = 500 ohm gain v_b/v_a = 5 v_a = v/5 rightarrow for given v_b = 5 volts v_a = 1volts v_a = 2.5 times R_4/R_3 + R_4 = 1 implies 2.5R_4 = R_3 + R_4 implies R_3 = 15R_4 for R_4 = 100 ohm implies R_3 = 150 ohm when switch is closed v_b = 2.5v(t) and amplifier resistance is negligible initial current I_0(0) = 0amps finaol current I_0(infinity) = -2.5/4 = -0.62amps time constant tau = L/R = 10mH/4 = 2.5mRc current I_out(t) = I_out(infinity) + (I_out(0) - I_out(infinity))e^-t/tau = -0.625 + (0 - (- 0.625))e^-t/2 sin I_out = 0.625(e^-400t - 1)amps for (t greaterthanorequalto 0), switch 2 on at t = 0 steads state voltage across the motor is -