Discrete-time induction machine current PI controller
Simscape / Electrical / Control / Induction Machine Control
The Induction Machine Current Controller implements discrete-time proportional-integral (PI) based induction machine current control in the rotor d-q reference frame. You typically use the Induction Machine Current Controller in a series of blocks that make up a control structure. For example, to convert the dq0 reference frame output voltage to voltage in an abc reference frame, connect the Induction Machine Current Controller to an Inverse Clarke Transform in the control structure.
The block uses the backward Euler discretization method.
Two PI current controllers that are implemented in the rotor reference frame produce the reference voltage vector:
, and are the d-axis and q-axis reference voltages, respectively.
, and are the d-axis and q-axis reference currents, respectively.
and are the d-axis and q-axis currents, respectively.
Kp_id, and Kp_iq are the proportional gains for the d-axis and q-axis controllers, respectively.
Ki_id and Ki_iq are the integral gains for the d-axis and q-axis controllers, respectively.
vd_FF, and vq_FF are the feedforward voltages for the d-axis and q-axis, respectively. The feedforward voltages are obtained from the machine mathematical equations and provided as inputs.
Ts, is the sample time of the discrete controller.
Saturation is imposed when the stator voltage vector exceeds the voltage phase limit Vph_max:
where vd, and vq are the d-axis and q-axis voltages, respectively.
In the case of axis prioritization, the voltages v1 and v2 are introduced, where:
For d-axis prioritization — v1 = vd and v2 = vq.
For q-axis prioritization —v1 = vq and v2 = vd.
The constrained (saturated) voltages and are obtained as:
and are the unconstrained (unsaturated) voltages.
v2_max is the maximum value of v2 that does not exceed the voltage phase limit. The equation that define v2_max is
In the case of d-q equivalence, the direct and quadrature axes have the same priority, and the constrained voltages are:
An anti-windup mechanism is employed to avoid the saturation of the integrator output. In such a situation, the integrator gains become:
where Kaw_id, Kaw_iq, and Kaw_if are the anti-windup gains for the d-axis, q-axis, and field controllers, respectively.
The plant model for the direct and quadrature axes can be approximated with a first-order system.
idqRef— Reference currents
Desired d- and q-axis currents for control of the induction machine, in A.
idq— Measured currents
Actual d- and q-axis currents of the controlled induction machine, in A.
vdqFF— Feedforward voltages
Feedforward pre-control voltages, in V.
VphMax— Maximum phase voltage
Maximum allowable voltage in each phase, in V.
Reset— External reset
External reset signal (rising edge) for integrators.
vdqRef— Reference voltages
Desired d- and q-axis voltages for control of the induction machine, in V.
D-axis current proportional gain— d-axis proportional gain
Proportional gain for direct-axis current control.
D-axis current integral gain— d-axis integral gain
Integral gain for direct-axis current control.
D-axis current anti-windup gain— d-axis anti-windup gain
Anti-windup gain for direct-axis current control.
Q-axis current proportional gain— q-axis proportional gain
Proportional gain for quadrature-axis current control.
Q-axis current integral gain— q-axis integral gain
Integral gain for quadrature-axis current control.
Q-axis current anti-windup gain— q-axis anti-windup gain
Anti-windup gain for quadrature-axis current control.
Sample time (-1 for inherited)— Block sample time
-1(default) | positive scalar
Time, in s, between consecutive block executions. During execution, the block produces outputs and, if appropriate, updates its internal state. For more information, see What Is Sample Time? and Specify Sample Time.
If this block is inside a triggered subsystem, inherit the
sample time by setting this parameter to
-1. If this block is in a
continuous variable-step model, specify the sample time explicitly using a positive
Axis prioritization— Axis prioritization for voltage limiter
Prioritize or maintain the ratio between the d- and q-axes when the block limits voltage.
Enable pre-control voltage— Pre-control voltage
Enable or disable pre-control voltage.