cscript_controller.pdf

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PLECS
Tutorial
Introduction to the C-Script Block
Implementation of a digital and analog PI controller
Tutorial Version 1.0

1 Introduction
The C-Script block is a versatile tool in the PLECS component library that can be used for implement-
ing custom controllers and components. The advanced capabilities of the C programming language
combined with the flexible sample time settings in the C-Script block allow almost any custom com-
ponent model, from a simple mathematical function to a complex state machine, to be implemented.
The C-Script block can also simplify the workflow when writing C code for DSP controllers since the
code can be reused for the DSP. The key skills that you will learn in this exercise are:
• Understand how the C-Script block interfaces with the simulation engine through function calls.
• Understand the different time settings available in the C-Script block.
• Use the C-Script block for implementing a mathematical function.
• Use the C-Script block for implementing a discrete and continuous PI controller.
Before you begin Ensure the file buck_converter.plecs is located in your working directory. You
should also have the reference files that you can compare with your own models at each stage of the
exercise.
2 Function Call Interface
The C-Script block interfaces with the simulation engine using a number of predefined function calls.
These function calls are depicted in Fig. 1. Each function call corresponds to a code window in the
C-Script editor, which is accessed from a pull-down menu. The most commonly used code windows
are described below, and for a complete description, one can refer to the PLECS User Manual or the
block’s documentation, which is accessed by clicking the Help button.
code declarations() In addition to the function windows, a Code declarations window is pro-
vided for defining global variables, macros and helper functions to be used in the C-Script block func-
tions. The code declarations code is essentially a global header file. All variables and functions defined
within this window are globally visible to all functions within the C-Script block.
start() The Start function code window is for initializing the simulation. Internal state variables,
for example, should be initialized here.
output() The Output function code window is designed to contain the functional code for the C-
Script block. A call is made to this function at least once during each simulation time step. For this
reason, any internal states or persistent variables should be updated in the update function.
update() If a model contains discrete internal states, a call is made to the code in the Update func-
tion code window directly after the output function has been executed. When the C-Script contains
internal states, they should be updated in this function rather than in the output function to ensure
they are updated only once during each time step.
3 Parameters
When you open the C-Script block the Setup tab of the code editor window as shown in Fig. 2 will ap-
pear. In this window you can configure the parameters. You will actually write your C code within the
function windows contained in the Code tab.
3.1 Sample time parameter
The Sample time setting is a key parameter that controls when the C-Script block is called. The sam-
ple time can be inherited from the simulation engine or controlled by the C-Script block itself. A de-
scription of the possible sample time settings is given below:
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Calculate
outputs
Calculate
updates
Calculate
outputs
Calculate
outputs
Start
simulation
Terminate
simulation
Main
loop
Event
detection
loop
Integration
loop
Calculate
derivatives
Calculate
zero-crossings
Figure 1: Function calls made during operation of the C-Script block. The update function is called
when discrete states are defined and the derivative function is called when continuous states
are defined.
Figure 2: C-Script editor window for configuring parameters and writing code.
Continuous The continuous time setting is selected by entering 0 into the sample time dialog. With
the continuous time setting, the time steps are inherited from the solver. Every time the solver takes a
step, the C-Script block is executed.
Discrete The discrete-periodic time setting is selected by entering a positive number into the sample
time dialog. The C-Script block is executed at discrete regular intervals defined by this sample time.
Variable The variable time setting is selected by entering -2 into the sample time dialog. With the
discrete-variable time setting, the next time step is determined dynamically by the C-Script block it-
self by setting the NextSampleHit built-in macro. The NextSampleHit must be initialized at the begin-
ning of the simulation to a value greater than or equal to the CurrentTime macro. See below for more
information on macros in the C-Script block.
3.2 Other parameters
The other parameters are described completely in the C-Script block’s documentation. However, it is
worth noting the following at this stage. When creating a C-Script block that contains static variables,
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you can add discrete states to create global static variables. The discrete states are accessed using a
macro command DiscState.
3.3 List of commonly-used macros
The C-Script block contains a number of built-in macro functions that can be used to interact with the
model or solver. Some of the commonly used macros are:
InputSignal(j, i) Reference the ith signal of the jth C-Script block input.
OutputSignal(j, i) Reference the ith signal of the jth C-Script block output.
DiscState(i) Reference a discrete state with index i.
NextSampleHit Set the next call time for the C-Script block. This variable is used
when the variable sample-time setting is active.
CurrentTime Retrieve the current simulation time.
SetErrorMessage(”msg”) Abort the simulation with an error message.
4 Exercise: Implement a Mathematical Function
In this exercise, you will use the C-Script block to implement the sine function with an offset value.
Your Task:
1 Create a new simulation model, and place a C-Script component and two Constant source blocks
into it. Label the first Constant block “Offset” and set its value to 0.5. Label the second Constant
block “Frequency” and set its value to 2π · 50. Use a Signal Multiplexer block to route the two con-
stant values into the C-Script block. Your simulation model should look like that shown in Fig. 3.
Frequency
Value: 2*pi*50
C
Value: 0.5
Oﬀset
0.5
C-Script
C-Script Scope
Figure 3: Implementing the function y = 0.5 + sin(2π50 · t) with the C-Script block.
2 You will then need to configure the C-Script block and write the code. To configure the C-Script
block, open the block by double-clicking and in the Setup tab set the Number of inputs to 2 and
the Number of outputs to 1. Set the Sample time setting to 0 to select a continuous, or inherited
sample time. To write the sine function you will need to use the cmath library (math.h header). In
the Code declarations window of the Code tab, enter the following code:
#include <math.h>
#define offset InputSignal(0,0)
#define freq InputSignal(0,1)
In the Output function code window, enter the following code to create the sine function:
OutputSignal(0,0) = sin(freq*CurrentTime) + offset;
3 Run the simulation: Set the simulation parameters of the PLECS solver to the following:
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• Simulation stop time: 20e−3 ms.
• Maximum step size: 1e−4 s
When you run the simulation, you should see a sine wave with a period of 20 ms and a vertical off-
set of 0.5 V.
At this stage, your model should be the same as the reference model, sine_wave.plecs.
5 Exercise: Implement a Digital PI Controller
In this exercise, you will replace a continuous proportional-integral (PI) voltage controller for a buck
converter with a digital PI controller. The continuous PI voltage controller for the buck converter is
depicted in Fig. 4. The continuous PI control law is described by the function:
y(t) = kpe(t) + ki
t
ˆ
0
e(τ) dτ (1)
In order to implement a digital PI controller using the C-Script block, you will need to use a discrete
form of the PI control law. The simplest way to discretize the PI controller is to use the backwards
rectangular rule to approximate the integral term with:
ik = ik−1 + Tsek (2)
where ik is the value at sample number k and Ts is the sample time. Thus the digital PI control law
becomes:
yk = kpek + kiik (3)
ki
kp
1/s
y
e
+
+
Figure 4: Continuous PI voltage controller.
5.1 Configure the C-Script block
Your Task: Open the buck converter model buck_converter.plecs and look at the implementa-
tion of the continuous PI voltage controller. Save a copy of the buck converter model before you
proceed with the following steps:
1 Look under the mask of the PI controller by right-clicking on the component and selecting Look
under mask (or use Ctrl+U) and delete all components except for the input and output ports.
Place a C-Script block directly between the input and output ports. Ensure the Number of inputs
and Number of outputs in the C-Script block settings are both set to 1.
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2 Add a parameter, Sample frequency (fs), to the PI controller mask and set its value to 25e3 Hz.
To add a parameter to the PI controller mask, right-click on the mask and select Edit Mask... (or
use Ctrl+M).
3 In the C-Script parameters, set the Sample time setting to 1/fs. This will cause the C-Script
block to execute at a discrete-periodic, or fixed sample rate of 1/fs.
4 The C-script code requires access to the parameters kp, ki and Ts. To pass these directly to the
C-Script block, enter them in the Parameters box that is displayed in the Setup tab. Enter the
variables kp, ki, 1/fs into the Parameters box.
5 Switch to the Code tab and in the Code declarations function define the following variables
static double kp, ki, Ts;
6 In the Start function assign the input parameters to the defined variables:
kp = ParamRealData(0,0);
ki = ParamRealData(1,0);
Ts = ParamRealData(2,0);
7 In the Code declarations function, also map the error input signal to the variable ek:
#define ek InputSignal(0,0)
5.2 Implement the digital control law using a discrete state
Your Task: The control code should be written in the Update function, since this is only called
once per sample period. On the other hand, the Output function is typically called several times
per sample period. Therefore, any discrete states such as integrator values that are calculated in
the Output function will be incorrect.
1 In the C-Script settings, set the Number of disc. states to 1. This creates a static internal vari-
able named DiscState(0) and causes the solver to invoke the Update function once every sample
period.
2 In the Code declarations function, define a global variable to represent the controller output, and
map the discrete state to a variable that represents the previous integrator value, ik−1.
double yk;
#define ik_1 DiscState(0)
Initialize ik−1 to 0 in the Start function. Note that yk needs to be a global variable since it is ac-
cessed in both the Update and Output functions.
3 In the Update function, define the variable double ik, which is used to store intermediate results.
Then implement the control law defined in Eq. (2) and (3). Don’t forget to add ik_1 = ik; after
calculating ik.
4 In the Output function, assign the result of the control law calculation, to the output
OutputSignal(0,0) = yk. Note that the output can only be written to in the Output function.
When you run the simulation the output voltage should be the similar to the model with the continu-
ous PI controller.
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At this stage, your model should be the same as the reference model,
cscript_controller_1.plecs.
Note: The output of the digital PI controller is delayed by one cycle because the Update func-
tion is called after the Output function, as shown in Fig. 1. The Output function therefore out-
puts the result calculated in the previous time step. The exact sequence of function calls for this
simulation is depicted in Fig. 5. The number of calls to the Output function per time step is de-
termined internally by the solver. For this particular model, the Output function is called twice
during each major time step. However, for other models, the Output function may be called
more often.
Figure 5: Timing of function calls for cscript_controller_1.plecs.
Eliminate the one cycle delay
Your Task: The one cycle delay can result in instability if the sample frequency is too low. To
observe this effect, change the sample frequency to 10e3 Hz and rerun the simulation. To elimi-
nate the delay, ensure the control result is output in the same time step it is calculated.
1 Create a global variable, double ik, in the Code declarations function.
2 Remove the control code from the Update function except for the line updating the discrete state,
ik_1 = ik;
3 Shift the control code to the Output function:
ik = ik_1 + Ts*ek;
OutputSignal(0,0) = kp*ek + ki*ik;
In other words, the integral action is calculated in the Output function, but the running total,
recorded by the discrete state, is not updated until the Update function.
5.3 Implement the continuous control law
Although the primary function of the C-Script block is for implementing complex functions and dis-
crete controllers, it allows continuous states and differential equations to be defined for solving ordi-
nary differential equations of the form ẋ = f(x). The simulation engine solves the differential equation
using numerical integration. Since the integrator in Eq. (1) can be described by an ordinary differen-
tial equation:
di
dt
= e(t) (4)
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the integral action can be modeled in the C-Script block by defining a continuous state, i(t), and the
differential equation Eq. (4). At each time step the solver will calculate i(t) numerically.
For each continuous state that you define, the following macros are created: ContState(i) and
ContDeriv(i). These macros are the hooks that allow the simulation solver to solve the differential
equation. All you need to do is describe the equation in the Derivative function.
Your Task:
1 Create a copy of the model cscript_controller_2.plecs and reconfigure the C-Script settings.
Set the Sample time setting to 0 and remove the parameter 1/fs. Set the Number of disc.
states to 0 and the Number of cont. states to 1. The continuous state will be used to represent
the integral term in Eq. (1).
2 In the Code declarations function, change the InputSignal(0,0) mapping to e and map the con-
tinuous state and derivative to variable names with the following:
#define e InputSignal(0,0)
#define I ContState(0)
#define I_deriv ContDeriv(0)
3 In the Derivative function, you need to enter the differential equation that describes the integra-
tor. This is I =
´
e(t) dt or dI/dt = e(t), therefore enter I_deriv = e;. The solver will then solve
the differential equation to yield the integrator value, I.
4 The appropriate initial value for the integrator value I = 0 is set in the Start function.
5 Remove all code from Update functions, and in the Output function, remove all code except for
the following:
OutputSignal(0,0) = kp*e+ki*I;
When you run the simulation, you should see the same output voltage as with the original continuous
PI controller.
When to use a continuous state
In this example, implementing an integrator by creating a continuous state and defining a differen-
tial equation was more work than using the integrator component itself. However, working with con-
tinuous states inside the C-Script block allows you to add advanced functionality to differential equa-
tions or state-space systems. For example, you can implement an integrator that resets itself when
its output reaches a certain value. This is not possible using a standard integrator component with a
comparator, since feeding back the comparator output to the integrator reset port creates an algebraic
loop.
6 Advanced Exercise: Implement a Digital PI Controller with
Calculation Delay
In Section 5.2 you implemented a PI controller without a calculation delay. In a practical system, a
finite delay exists due to the time needed for the controller to read the input(s), perform the control
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calculation and write to the output(s). This delay can degrade the stability for certain systems. To
simulate this calculation delay, a delay time is introduced before the control result, yk, is written to
OutputSignal(0,0).
Your Task:
1 Save a copy of the model cscript_controller_2.plecs and add an additional parameter to the
voltage controller mask labeled Calculation delay. Assign this to a variable named td and set its
value to 0.1. This will be used to set the calculation delay time to 0.1Ts.
2 In the C-Script block settings, add the argument td/fs to the list of Parameters in the Setup tab
and define a variable Td in the Code declarations function:
static double Td;
and assign the value Td = ParamRealData(3,0); in the Start function.
3 To implement the calculation delay, you will first need to implement a hybrid discrete-variable,
sample time setting. The fixed-step setting will provide a sample hit at the beginning of each pe-
riod and the variable time step will provide a hit after the calculation delay. Hybrid time settings
must be entered as a matrix format, where the first entry in a row is the sample time and the sec-
ond entry is the offset time. Enter the following Sample time setting: [1/fs, 0; -2, 0]
4 To ensure the first hit time is generated by the fixed time step setting, you should initialize the
NextSampleHit macro, which defines the variable step hit time, to a large number in the Start
function: NextSampleHit = NEVER;
5 Note that you will need to define NEVER as a very large number in the Code declarations func-
tion. If you include the file <float.h> you can define NEVER as DBL_MAX, the largest machine repre-
sentable float number.
6 At the beginning of the switching cycle you will need to carry out the control calculations for ik and
yk. The calculated control action, yk, is not output until the next call to the Output function, which
will occur at the time CurrentTime + Td. Add the following lines in the Update function:
if (NextSampleHit == NEVER) //beginning of switching cycle
{
//Control calculations for ik, ik_1, yk here
NextSampleHit = CurrentTime + Td;
}
else
NextSampleHit = NEVER;
7 In the Output function, assign yk to the output port in order to output the control action that was
calculated at the beginning of the switching cycle.
cscript_controller_3.plecs. To observe the influence of the calculation delay, set fs to
10e3 Hz and run the simulation for a calculation delay of 0.1 and 0.9. Note that this implementa-
tion only allows values td ∈ ]0, 1[, the treatment of the special cases 0 and 1 is left for the user as an
additional exercise.
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7 Conclusion
In this exercise you learned how to use the PLECS C-Script block to implement a custom digital PI
controller with several adaptations. This involved having an understanding of the function calls that
are predefined in the block and are used in order to interface with the simulation engine. Another im-
portant aspect of the C-Script block is understanding the different time settings that are available for
configuration in the block, which are crucial for ensuring certain desired behavior such as dynamic
step size calls for timing functions or mimicking a fixed-step controller. The PLECS C-Script block is
highly versatile and can be used to model elaborate controllers and components.
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Revision History:
Tutorial Version 1.0 First release
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