Linearize Models with Converters Using Averaged Switching
Learn how to prepare models for linearization when your model contains a converter block. For an overview of linearization techniques, see Linearization Techniques for Control Design.
To prepare models with DC-DC converters for linearization, set the Switching
device parameter to
Averaged Switch and replace the
pulse-width modulation (PWM) signal with a modulation waveform. For a list of converter blocks
that support the
Averaged switch option, see List of Converter Blocks.
The default value of the Switching device parameter is
Semiconductor Switch. This value results in a model that you cannot linearize
exactly because discontinuities occur when the switching devices transition between the on and
off states. You can use the
Averaged Switch option to reduce the model
fidelity and linearize the model.
When you set the Switching device parameter to
Switch, the block models the switching device as a semiconductor switch with an
antiparallel diode. The control signal port G accepts values in the
interval [0,1]. When G is equal to
1, the averaged switch is fully opened or fully closed respectively. The
switch behaves similarly to the Ideal
Semiconductor Switch block with an antiparallel diode. When
G is between 0 and 1, the averaged switch is partly opened. You can
average the PWM signal over a specified period. You can then undersample the model and use
modulation waveforms instead of PWM signals.
After you set the Switching device parameter to
Switch and replace the PWM signal with a continuous signal, you can linearize your
model. For example, you can use the
linmod function. You can also use the steady state as an
operating point that is suitable for linearization. For more information about the
linearization techniques that you can now apply, see Linearization Techniques.
As an alternative to using blocks that support the
option, you can use low-fidelity, average-value converter blocks. You can linearize models
that contain these blocks. For a list of average-value converter blocks, see List of Converter Blocks.
For more complex models with discontinuities, you can estimate a linear model by running a dynamic simulation. For more information, see Estimate Linear Models from Simulation Results.
The Linearize DC-DC Converter Model example shows how to linearize a model of a DC-DC converter using averaged switching or an average-value converter.
These examples show how to use different levels of fidelity in DC-DC converters. In both examples, the lowest fidelity model with averaged switches and modulation waveforms is suitable for linearization, and you can use the steady state as an operating point.
The DC-DC Converter Model Fidelity Comparison example shows how to use different levels of fidelity in a Buck-Boost converter:
Highest fidelity — Buck-Boost converter with ideal switches. The gate control signal input is a PWM signal.
Medium fidelity — Buck-Boost converter with averaged switches. The gate control input is a moving average of the PWM signal.
Lowest fidelity — Buck-Boost converter with averaged switches. The gate control input is a constant equal to the PWM duty cycle.
The Bidirectional DC-DC Converter Current Control example shows how to control the inductor current of a bidirectional DC-DC converter. The Bidirectional DC-DC Converter block uses averaged switches. To achieve different levels of fidelity, you can use gate pulses, averaged gate pulses or modulation waveforms.
List of Converter Blocks
You can use the
Averaged switch option in these blocks to linearize models:
Alternatively, you can use these low-fidelity, average-value blocks for linearization.
- Linearize DC-DC Converter Model
- DC-DC Converter Model Fidelity Comparison
- Bidirectional DC-DC Converter Current Control
- Power Converter Model Fidelity Comparison