Velocity Controller

Discrete-time velocity controller

Libraries:
Simscape / Electrical / Control / General Machine Control

Description

The Velocity Controller block implements a velocity controller in discrete-time.

You provide measured and reference rotor velocities (w and w_ref) as inputs to the block. The block then outputs a reference torque T_ref for an electric drive.

To prevent windup in the integrator, feed the saturated reference torque T_{ref_sat} from the electric drive back to the velocity controller.

Equations

You can control the rotor angular velocity with discrete sample time T_s using one of three common approaches:

Proportional-integral (PI) control, with proportional and integral gains K_{p_w} and K_{i_w}:

$T_{r e f} = (K_{p_w} + K_{i_w} \frac{T_{s} z}{z - 1}) (w_{r e f} - w)$
Proportional (P) control, with proportional gain K_{p_w}:

$T_{r e f} = K_{p_w} (w_{r e f} - w)$
P-PI control characterized by a double velocity feedback loop as shown in the following figure:

Here, the PI Controller block is structured as in the PI control strategy, and K_v is the proportional gain for a P controller.

Zero Cancellation

Using PI control results in a zero in the closed-loop transfer function, which can result in undesired overshoot in the closed-loop response. This zero can be canceled by introducing a zero-cancelation block in the feedforward path. The zero cancellation transfer function in discrete time is

$G_{Z C_w} (z) = \frac{\frac{T_{s} K_{i_w}}{K_{p_w}}}{z + (\frac{T_{s} - \frac{K_{p_w}}{K_{i_w}}}{\frac{K_{p_w}}{K_{i_w}}})}$

Examples

IPMSM Torque Control in a Series-Parallel HEV

A simplified series-parallel hybrid electric vehicle (HEV). An interior permanent magnet synchronous machine (IPMSM) and an internal combustion engine (ICE) provide the vehicle propulsion. The ICE also uses electric generator to recharge the high-voltage battery during driving. The vehicle transmission and differential are implemented using a fixed-ratio gear-reduction model. The Vehicle Controller subsystem converts the driver inputs into torque commands. The vehicle control strategy is implemented as a Stateflow® state machine. The ICE Controller subsystem controls the torque of the combustion engine. The Generator Controller subsystem controls the torque of the electric generator. The Drive Controller subsystem controls the torque of the IPMSM. The Scopes subsystem contains scopes that allow you to see the simulation results.

Open Model

IPMSM Velocity Control

Control the rotor angular velocity in an interior permanent magnet synchronous machine (IPMSM) based automotive electrical-traction drive. A high-voltage battery feeds the IPMSM through a controlled three-phase converter. The IPMSM operates in both motoring and generating modes according to the load. An ideal torque source provides the load. The Scopes subsystem contains scopes that allow you to see the simulation results. The Control subsystem includes a multi-rate PI-based cascade control structure which has an outer angular-velocity-control loop and two inner current-control loops. The task scheduling in the Control subsystem is implemented as a Stateflow® state machine. During the one-second simulation, the angular velocity demand is 0 rpm, 500 rpm, 2000 rpm, and then 3000 rpm.

Open Model

HESM Velocity Control

Control the rotor angular velocity in a hybrid excitation synchronous machine (HESM) based electrical-traction drive. Permanent magnets and an excitation winding excite the HESM. A high-voltage battery feeds the HESM through a controlled three-phase converter for the stator windings and through a controlled four quadrant chopper for the rotor winding. An ideal torque source provides the load. The Control subsystem includes a multi-rate PI-based cascade control structure. The control structure has an outer angular-velocity-control loop and three inner current-control loops. The Visualization subsystem contains scopes that allow you to see the simulation results.

Open Model

Ports