Simulation essentials with Simulink

Table of Contents

This note provides in-depth content for an accurate and efficient offline simulation of an imperix controller and the corresponding plant model using ACG SDK on Simulink.

A general overview of software-related notes is given on this page.

Fundamental concepts

The offline simulation is meant to reproduce as faithfully as possible the behavior of the overall system (controller and plant). To that end, the Simulink blockset was designed with the following guidelines in mind:

The plant quantities are to be modeled with continuous signals
- This requires a variable-step solver
The control algorithm is modeled with discrete signals, sampled at a rate equal to the interrupt frequency, and with a phase corresponding to the sampling phase.
- This requires a discretized algorithm (in $z$ domain)
- This is modeled accurately with the variable-step solver, as it is forced to take a major step at each execution of the interrupt
The behavior of the real PWM generators is modeled, in particular:
- The frequency and phase of the carrier
- The instants when the duty-cycle and phase parameters are updated (at zero and/or max of the carrier)
The duration of the algorithm execution is modeled
- This induces a delay between the start of the interruption and the availability of the new data

With all the phases and delays modeled accurately, the simulated controller has the same dynamics as the real controller, which allows tuning the control parameters during the offline simulation.

The imperix blockset is already implemented such that these guidelines are automatically observed. As such, no particular action is required from the user.

Working principle of the main blocks

The three fundamental blocks are the Configuration, ADC, and PWM blocks. Most applications can work with only those three, as in the standard configuration shown below.

Clock and Configuration

The Configuration block configures the main global parameters of the model, such as

The model execution purpose (offline simulation or code generation for a real-time target)
The frequency of CLOCK_0 (sampling and interrupt clock)
The interrupt phase and postscaler

To configure and implement CLOCK_0, the Configuration block contains a Clock block. A clock is a time base serving as a time reference for different peripherals (e.g. ADC or PWM).

In simulation, the Clock block outputs a sawtooth signal with the clock period $T_{clk0}=1/f_{clk0}$ and a phase of zero. Then, this clock signal is passed through a subsystem that generates a sampling clock, with a relative phase-shift of $\phi_s$ and a period defined by

$$T_s = \left\{ \begin{array}{ll} T_{\text{clk0}} & \text{if postscaler = 0}\\ 2\cdot \text{postscaler}\cdot T_{\text{clk0}} & \text{otherwise} \end{array}\right.$$

Finally, the configuration block sets the value of the sample time variable

$$\text{CTRLPERIOD} = \left[T_s, \phi_s T_s\right]$$

This variable can be used in any block requiring a sample time (e.g. discrete transfer functions) to make sure it is executed at the interrupt frequency and with the proper phase.

The fundamental elements of the Configuration block are mapped below, with the waveform of the generated signals.

ADC

The ADC block allows retrieving the sampled value of a given ADC channel and converts it to its value in physical unit.

The simulation model simply sample-and-holds the input signal (2) with the rising edges of the sampling clock (1). The input signal is typically a continuous signal coming from the plant model and representing a measurement value. The sample time of the output signal (3) is set to CTRLPERIOD in order to be automatically propagated to other connected blocks.

PWM

Various types of pulse-width modulators exist within the imperix blockset.

Among them, the carrier-based PWM modulator (CB PWM block) configures the corresponding FPGA peripheral and generates the PWM signals according to the duty-cycle and carrier phase parameters.

In the simulation model, the clock signal (1) connected to the clock input is used as a time reference to generate the carrier signal (2). In parallel, the duty-cycle value (3) is sampled once or twice per switching period (depending on the update-rate parameter) and compared with the carrier to produce the output PWM signal (5). (A more complex model is used to generate a carrier with a variable phase, which is beyond the scope of this document.)

Mastering the sample times

Mastering the sample time (essentially the execution rate) of each block is key for an accurate and efficient simulation, as well as the generation of proper run-time code. In particular, the execution rates must comply with the fundamental concepts listed above, namely:

The plant (i.e. physical) signals are represented by continuous signals
The control signals (i.e. those computed during the controller main interrupt) are represented by discrete signals with a sampling rate and phase corresponding to the configuration of the main interrupt. Their sample time is, therefore, the vector CTRLPERIOD.

The blocks of the library are built in such a way that they comply with these concepts. The user is only recommended to make sure that his control implementation is executed at the proper rate. In some situations, the CTRLPERIOD may not be propagated automatically to the whole control model (see the example of the step block below).

Verifying the sample times

In Simulink, the sample time of each signal can be displayed by choosing Display > Sample Time > Colors. The color legend can be displayed by pressing Ctrl+J (see below)

In Simulink, the sample time of “continuous” signals (as opposed to discrete signals with a fixed period) can either be Continuous or Fixed in Minor Step. The latter is essentially an optimized version of “continuous,” applicable when the value of the signal cannot change between the major steps of the solver. For instance, the PWM signals do not vary between the switching instants. They can be considered as “semi-continuous” signals. For further reading, see https://mathworks.com/help/simulink/ug/types-of-sample-time.html.

With the colors defined above, a typical control implementation should look like this:

Typical sample times of a simulation model

As the ADC and PWM blocks serve as an interface between the continuous plant signals and the discretized control, they contain blocks with different sample times and have thus a Hybrid sample time.

Altering the sample times

In most cases, inherited sample time (-1) ensures that the whole discretized control is executed at the proper rate. The illustration below shows a discrete PI controller whose sample time is -1 and the sample time is correctly propagated from outside the system:

Product notes > PN135: Simulation essentials with Simulink > sample_time_-1.png

In some cases, a certain block can enforce a wrong sample time, as in the example below, where the step block is continuous (its default sample time) and propagates the wrong sample time to the PI controller (in this case, this even results in an error, since the discrete PI cannot run at a continuous sample time):