Voltage Source–Based Current Regulation
7.6 Voltage Source–Based Current Regulation
Michael Giesselmann
In motor drive applications, it is often desired to control directly the input current of the motor to control the torque. DC control also limits dynamics resulting from the electrical characteristics of the machine. Controlling the torque provides direct control over the angular acceleration, which is essential for precise motion control. Current control is typically performed in the innermost loop of a cascaded feedback control loop arrangement [1]. However, most power electronics converters are circuits with controllable voltage output. To achieve current control, the voltage of the power electronics converter can be controlled in such a way, that the desired current is obtained. Several methods can be used to achieve this:
• A feedback control loop, typically using a PI controller can be used control the current. • The necessary voltage can be calculated in real time and applied to the motor. • The necessary voltage for fast transients can be calculated in real time and applied to the motor
and the residual error can be corrected by a PI controller. Examples illustrating each of the schemes are described in the following. Figure 7.19 shows an example
of a DC motor in which the current is controlled by adjusting the applied voltage using a PI controller such that the current follows the desired trajectory. The result is presented in Fig. 7.20 , which shows that the current indeed follows the desired value at all times.
Sometimes even better results and higher loop bandwidth can be obtained if known information about the motor and the load is used to calculate the required voltage in real time. Figure 7.21 shows some fundamental equations of a permanent magnet (PM) DC motor. Here a capacitor is used to represent the kinetic energy stored in the machine. Therefore, the second voltage loop equation in Fig. 7.21 represents the voltage across the motor at all times. To test this theory, the “compensator” in the circuit shown in Fig. 7.22 calculates this voltage and applies the result to the DC motor. The subcircuit of the
FIGURE 7.19 Voltage source–based current control using a PI feedback loop.
FIGURE 7.20 Simulation result for the circuit shown in Fig. 7.19 .
V s =R rot⋅ I rot +L −I d rot⋅ rot +K m⋅ ω
Voltage loop equation
dt
− ⋅ J ⋅ ω 2 =− 1 ⋅ C eq ⋅ E 2 C eq = J ⋅ ω
2 2 E 2 K 2 m Equivalent Capacitance
V s =R
+L rot⋅ d I rot rot⋅ −I + − 1 ⋅
dt rot C eq
I rot dt
Voltage loop equation
FIGURE 7.21 Fundamental equations for the PM DC machine.
FIGURE 7.22 Voltage source–based current control using a feedforward approach. compensator is shown in Fig. 7.23 . The result is identical to that shown in Fig. 7.20 . However, for the
correct implementation of this scheme, the load and the inertia of the system needs to be known precisely, which is not realistic. Therefore, the best strategy is to implement the first two terms on the right side of the second voltage loop equation in Fig. 7.21 using a compensator and to use a PI controller to eliminate the residual error.
The advantage of the mixed (compensator and PI residual controller) approach is that the fast dynamics are covered by the feedforward path through the compensator, whereas the effect of the slower integral term is taken care of by the PI controller. The compensator will immediately apply the correct voltage to overcome the ohmic resistance of the winding and to establish the correct current slope in the rotor induc- tance. As the machine accelerates, the PI controller adds the appropriate voltage to offset the back-emf
FIGURE 7.23 Subcircuit for the compensator shown in Fig. 7.22 .
FIGURE 7.24 Voltage source–based current control using a feedforward approach for the fast transients and a PI controller for the residual error.
of the motor. An example for this approach is shown in Fig. 7.24 . Again, the results are identical to the ones shown in Fig. 7.20 .
Reference
1. Mohan, N., Electric Drives, An Integrative Approach, MNPERE, Minneapolis, MN, 2001.