5.3: DC-Motor Drive Circuits

Learning Objectives

After completing this section, you will be able to:

1. Explain both low- and high-side DC-motor drive circuits.
2. Describe a PWM (pulse-width modulation) high-side drive circuit and its working principle.
3. Explain the working principle of an H-bridge circuit driven by the PWM signals.

This section discusses how to drive the DC motor efficiently using a PWM (pulse-width-modulated) signal in either a single or double direction. Single direction uses a high-side or low-side drive whereas dual-direction uses an H-bridge drive. Figure 5.19 illustrates the single-direction (or one-direction) drive. The figure’s left plot shows a low-side drive and the right plot shows a high-side drive.

The current (or voltage) regulator is used to regulate the DC-motor armature current \(i_a\) to achieve the desired motor torque; the motor torque output is proportional to its armature current. In Section 4.6, we briefly introduced a sample low-side DC-motor drive circuit (see Figure 4.57), where an operational amplifier and a transistor are used to regulate the motor armature current. The principle of the low-side drive (or high-side) is to regulate the voltage drop \(v_{reg}\) on the voltage or current regulator (see Figure 5.19) so that the DC-motor armature voltage \(v_a=V_{bat}-v_{reg}\) results in the desired armature current \(i_a\) (or DC-motor output torque \(τ\)).

The type of transistor used in the current regulation circuit is a primary factor in selecting a low-side or high-side drive. For example, an NPN (negative-positive-negative) transistor is often used to construct the low-side drive circuit (see the left plot of Figure 4.57). A PNP (positive-negative-positive) transistor is for the high-side drive circuit.

A sample high-side drive circuit is shown on Figure 5.20. One operational amplifier (on the right side, marked “Feedback isolation circuit”) is used to generate the feedback voltage drop on resistor \(R_s.\) Another operational amplifier is used for feedback control of the motor armature current. The control circuit is intended to have the following relationship

\[v_{ref}=V_{bat}-v_e\approx R_si_a\ \to \ i_a\approx \dfrac{v_{ref}}{R_s} \label{5.26}\]

due to the following relationship from the feedback isolation circuit.

\[\dfrac{v_e-0.5V_{bat}}{R_f}=\dfrac{0.5V_{bat}-v_{ref}}{R_f} \label{5.27}\]

In this case, a desired armature current can be achieved by setting \(v_{ref}\) as follows.

\[v_{ref}=i_{a-desired}R_s\ \label{5.28}\]

where \(i_{a-desired}\) is the desired armature current. We are now ready to discuss the PWM drive for low-side and high-side PWM drive circuits. The low-side PWM drive circuit was previously presented in Figure 4.57; the associated benefit of a PWM drive were addressed in Example 4.20 in Section 4.6. Here, we will discuss only the high-side drive PWM circuit. To utilize the PWM signal, the transistor is often replaced by MOSFET (metal oxide semiconductor field-effect transistor) or IGBT (insulated-gate bipolar transistor) because of their fast-switching capability.

Figure 5.21 presents a sample high-side drive circuit for DC motors. Here, transistor \(T_i\) is used to inverse the PWM signal with isolation. The diode \(D_i\) is used to improve the circuit robustness to ground noise; as a result, the circuit requires about 1.4 volts to turn on transistor \(T_i\) (instead of 0.7 volt in case without \(D_i\)). After the transistor \(T_i\) is turned on, the collector voltage is reduced to about 1.0 volt; as a result, the drive transistor \(T_d\) is turned on and supplies power to the DC motor. When the input voltage \(v_{pwm}\) is low, transistor \(T_i\) is turned off and so is transistor \(T_d\), leading to no power supplied to the DC motor. Note that the diode \(D_m\) is used to allow the motor current to flow when transistor \(T_m\) is turned off. The reason is that the motor current cannot be changed instantly due to its armature winding inductance. Examples 5.8 and 5.9 focus on analog and PWM high-side drive circuits, respectively.

Example 5.8

For the analog high-side drive circuit presented on Figure 5.20, with the sensing resistor value of \(0.2\ Ω\), find the reference voltage \(v_{ref}\) to achieve the target DC-motor armature current of \(i_a=5\ A\). From equation \ref{5.28} we have the following.

\[ v_{ref}=i_{a-desired}R_s=5\times 0.2=1.0\ V \label{5.29}\]

Therefore, the reference voltage \(v_{ref}\) is \(1.0\ V\).

Example 5.9

Assume that reference \(v_{pwm}\) is a 0 to 5 volts PWM with its duty-cycle of 40%, the battery voltage is \(V_{bat}=12.2\ \)volts, DC-motor armature resistance \(R_a\) is 0.1 \(Ω\), and the voltage drop of transistor \(T_m\) in Figure 5.21 is \(v_{e2c}\)= 0.2 when it is fully turned on. Find the resulting armature current in Figure 5.21. Note that with a duty-cycle of 40% for the input PWM reference signal, the transistor \(T_m\) will be turned on with a 40% duty-cycle. When the transistor \(T_m\) is turned on, the DC-motor armature current is shown below.

\[\ i_{a-on}=\dfrac{V_{bat}-v_{e2c}}{R_a}=\dfrac{12.2-0.2}{0.1}=120\ A \label{5.30}\]

With the 40% duty-cycle, the averaged motor armature current is shown below.

\[i_a=i_{a-on}\times 40\%=120\times 0.4=48\ A \label{5.31}\]

Having discussed low-side and high-side DC-motor drive methods, let’s now look at the H-bridge drive for DC motors. Compared with the H-bridge drive, the main disadvantage of low- and high-side drive methods is that the applied armature voltage direction cannot be altered. That is, it is impossible to change the armature current direction due to fixed armature voltage direction. As a result, the torque generated by the DC motor will maintain in one direction. This makes the control torque of the mechatronic system in one direction, which limits the capability of the motor speed control (to be discussed in this section).

Figure 5.22 shows the architecture of an H-bridge drive system, where the diodes are used to protect switches right after the switches are turned off. The DC-motor armature winding has a certain inductance such that the armature current cannot be set to zero instantaneously. These diodes provide a path to allow the armature current flow so that the voltage on these switches will not increase to the level damaging the switches. When driving the DC motor in one direction, we need to activate a pair of the switches represented by a circle with contact. For example, to generate an armature current flow from left to right for the DC motor in Figure 5.22, the upper-left and lower-right switches need to be turned on. In this case, we can see that the H-bridge drive looks like the combined high-side and low-side drives discussed earlier. Note that the high-side (or low-side) drive has a switch on the high-side (or low-side).

Figure 5.23 shows how the four-switch H-bridge drive can be used to drive the DC motor in forward (clockwise) and backward (anticlockwise) directions for both rotational directions. Recall that the DC motor can be controlled by the applied armature voltage (or current) to the H-bridge circuit using pulse-width-modulation (PWM) signals. That allows the equivalent armature voltage (or current) to be regulated by PWM signal duty-cycle in the same way as that used for the high-side or low-side PWM drive.

To regulate the motor direction, a pair of the switch needs to be turned on simultaneously. To turn the DC motor forward in the clockwise direction (see the left drawing), we turn on the upper-left and lower-right switches (marked by red energized switches), resulting in the marked armature current in Figure 5.23. To turn the DC motor backward in the anticlockwise direction (see the right drawing), we turn on the upper-right and lower-left switches simultaneously (marked by red energized switches), resulting in the marked armature current in Figure 5.23. When the motor is activated, these four diodes are not activated because the current flows in the opposite direction to the diode conducting one.

Another mode of operation is braking regeneration for the four-switch H-bridge. Figure 5.24 shows two operational modes for braking regeneration. One is when the motor is rotating forward (the left drawing) and the other is backward (the right drawing).

Consider the case of braking regeneration when the motor is rotating in the forward direction. We can see that only the lower-right switch is turned on and there is no applied armature voltage. In this case, the back EMF voltage (\(K_mω\)) is in the opposite direction of the battery. As a result, the armature current flows from right to left of motor to the battery due to activated upper-left red diode, which charges the battery. In addition, for braking regeneration, the upper-left switch cannot be turned on. If so, with both upper-left and lower-right switches turned on, the DC motor is in the drive mode.

The right drawing shows the case of braking regeneration when the motor is rotating in the anticlockwise (backward) direction. The analysis is similar to the case when the motor rotates in the clockwise (forward) direction; we will not repeat it here.

Example 5.10

Consider the braking regeneration when the motor rotates in the clockwise (forward) direction. In the left drawing of Figure 5.24, we can achieve braking regeneration by turning on only the lower-right switch. Now let’s find another operational mode for braking regeneration, with the motor rotating in the clockwise (forward) direction, but different from turning on the lower-right switch. We can implement this other operational mode by turning on the upper-left switch, as illustrated in Figure 5.25.

Table 5.2 summarizes the four-switch H-bridge operational mode. Note that during the braking regeneration, a charge control circuit will be implemented to harvest the regeneration energy at low motor speed.

Table 5.2: Four-switch H-bridge operational modes.

Upper left	Upper right	Lower left	Lower right	Description
On	Off	Off	On	Forward running
Off	On	On	Off	Backward running
Off	Off	Off	On	Forward regeneration
On	Off	Off	Off	Forward regeneration
Off	Off	On	Off	Backward regeneration
Off	On	Off	Off	Backward regeneration

Figure 5.26 presents a sample four-switch H-bridge drive circuit for DC motors, where eight transistors and four diodes are used. Transistor \(T_s\) (e.g., TIP31) is used as a switch to handle a relatively large motor current. Transistor \(T_i\) (e.g., 2N3904) is used for amplifying an input PWM signal. Diode \(D_m\) is used for handling the current right after the switch transistor \(T_s\) is turned off as well as the current during braking regeneration.

Resistors \(R_i\) and \(R_l\) are input and amplifier load resistors, respectively. Note that, normally, \(R_i\gg R_l\). For example, \(R_i\) could be selected as 1.2 \(kΩ\) and \(R_l\) 65 \(Ω\). The sample circuit uses conventional transistor as the switch element. In many applications, MOSFET (metal-oxide-semiconductor field-effect transistor) and IGBT (isolated-gate bipolar transistor) are widely used to handle high-power switching.

Earlier in this section, we discussed using analog and PWM signals to drive the low- and high-side circuit of a DC motor. Now the question is whether the PWM control signal could affect the DC-motor speed or displacement response. Next, we will compare the difference between analog and PWM drive signals through a simulation study in Simulink [22].

Figure 5.27 shows two Simulink diagrams used for this study. The only difference between the top and bottom diagrams is the input (armature voltage) to the DC-motor model. The top plot has an analog voltage of 1.0 volt whereas the bottom plot has the PWM signal as input with a bottom-to-peak voltage of 5 volts and 20% duty-cycle. The equivalent voltage generated by the given PWM signal can be calculated below, using equation \ref{4.106} in Section 4.6.

\[v_{analog}=v_{bottom-peak}\times duty_{cycle}=5\times 0.2=1\ V \label{5.32}\]

In Figure 5.27 the motor torque coefficient \(K_τ=0.23\ Nm/A\) and the back EMF coefficient \(K_m=0.027\ V/(rad/s)\). The motor armature winding resistance is \(R_a=4.8\ Ω\) and the armature inductance is \(L_a=2\ mH\). For the mechanical part of model, the motor rotor inertia is \(J_m=0.0019\ kgm^2\) and the rotational friction coefficient is \(b_m=0.004\ Nm/(rad/s)\). You can find the corresponding coefficients in in Figure 5.27. To learn more about the graphic simulation software Simulink, see the MATLAB/Simulink website or reference [22].

Figure 5.28 provides Simulink simulation results. The left plot presents the step response (blue line) with an analog step input of 1 volt (red line). The right plot presents the step response (blue line) with a PWM step input of 20% duty-cycle with bottom-to-peak of 5 volts (red line and the zoomed-in PWM signal). For the analog step input, the response shown in the left plot converges to its steady state within 1.5 seconds. We can calculate the approximated DC-motor system time constant \(T\) using equation \ref{2.120} as below.

\[T=\dfrac{J_mR_a}{R_ab_m+K_τK_m}=\dfrac{0.0019\times 4.8}{4.8\times 0.004+0.23\times 0.027}=0.359\ second \label{5.33}\]

As a result, for this case, we can calculate the 2% settling time \(t_s(2\%)\) of the DC-motor system as below.

\[t_s(2\%)=4\times T=4\times 0.359=1.436\ second \label{5.34}\]

Therefore, the simulated system response for the analog step input is very close to the analytic settling time. Now, considering the PWM response on the right plot of Figure 5.28, we can see that the motor speed response (blue line) is almost identical to the analog step response (left plot). This is mainly because a 1-kHz PWM signal is used for the PWM step signal; the motor system with a time constant of \(T=0.359\) second basically filters out the pulsation of the PWM signal. Only the mean effect of the PWM signal, equivalent to a 1.0-volt analog step, remains.

Figure 5.29 shows a Simulink simulation diagram for closed-loop motor speed control. The right red-dashed box, DC-motor model, is the model given in Figure 5.27. The middle red-dashed box, PWM-drive model, converts the analog control signal generated by the PID controller into the zero-to-five volt PWM signal (500 Hz). The left red-dashed box, PID controller, is an analog PID controller (see Section 3.4). A negative feedback loop is formed by subtracting the motor output speed from the reference speed. This obtains the speed error signal to be used as the input to the PID controller with proportional gain \(K_p=5\), integral gain \(K_i=2\), and derivative gain \(K_d=0\).

Figure 5.30 presents the simulation results for the Simulink diagram shown in Figure 5.29. The top plot shows the analog control signal produced by the PID controller. The middle plot shows the PWM control signal. The bottom plot shows the time response of the DC-motor speed. The analog signal is saturated by \(\pm 10\) volts, where 10 volts corresponds to the 100% duty-cycle of zero-to-five-volt PWM signal. This results in the saturated PWM signal. From the middle plot, we can see that the PWM control signal is saturated between zero and 0.19 second to accelerate the motor speed at it maximum PWM duty-cycle of 100%. As the motor speed approaches the reference speed of 20 \(rad/s\), the PWM duty cycle reduces to about 50%, with the analog control signal close to 5 volts. The bottom plot shows that the settling time with closed-loop control is about 0.2 second, compared with the open-loop case of about 1.5 second; see equation \ref{5.34}. This indicates that closed-loop control can significantly reduce the motor speed response time.

Before ending this section, let’s consider a class of actuators called servomotors. A servomotor is a closed-loop angular displacement control system. It consists of a DC- (or AC-) motor actuator, a gear system to reduce motor speed, a displacement sensor (e.g., voltage divider) for measuring the angular displacement, and motor control electronics for regulating the angular displacement. Figure 5.31 shows a small servomotor system using a DC motor.

Servo motors have several advantages. They have high intermittent torque output, high torque to inertia ratio, and fast response speed. They are good for angular velocity and position control. Servo motors are available in all sizes and they have smooth rotation at low speed due to gearbox. Servo motors also have disadvantages. They are more expensive than stepper motors for displacement control. They require tuning control loop for optimal performance. Furthermore, they are not suitable for either hazardous environment or excessive power (load) applications that could result in partially damaging DC servo motor.

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