Skip to content

PID Controller.

Introduction.

The PID Controller is implemented here in a Standard form.

pid block diagram
bloc diagram of standard form of a continuous PID with filtered derivative

Parameters:

Here the continuous transfer function representation of the PID.

\[command = K_p . \left( \varepsilon + \dfrac{1}{T_i.s} . \varepsilon + \dfrac{T_d.s}{1 + \frac{T_d}{N}.s}.\varepsilon \right)\]

where:

  • \(K_p\) is the proportionnal gain
  • \(T_i\) is the integration time
  • \(T_d\) is derivative time
  • \(N\) help to filter the derivative (typical values \(\in [2, 20]\)).

controller are sampled

We show here the continuous form of the function we want to implement. But calculation are sampled. Relationship to Laplace transform

Discretization:

This Pid() object is implemented using a backward euler integration method.

We have the following discrete equation implemented:

\[ \begin{align} \epsilon_k &= y_{ref_{k}} - y_{meas_{k}} \\ \\ i_k &= i_{k-1} + T_s . \epsilon_k \\ \\ d_k &= \dfrac{\epsilon_k - \epsilon_{k-1}}{T_s} \\ \\ f_{d_k} &= (1 - e^{-T_s/\tau}) . d_k + e^{-T_s/\tau} . f_{d_{k-1}} \end{align} \]
\[ u_k = K_p .\left( \epsilon_k + \dfrac{1}{T_i} . i_k + T_d . f_{d_k}\right) \]

Use of the PID Controller.

The use of the Pid is based on 3 steps.

  1. Object instanciation (declaration).
  2. Initialisation.
  3. Execution.

Example

For each Controller like (Pid, Rst, Pr) we have to define a parameter structure.

We define constants used to initialize the parameter structure. 

#include "pid.h"

static float32_t Ti = 7.5175e-5F;
static float32_t Td = 0.0F;
static float32_t N = 0.0F;
static float32_t upper_bound = 1.0F;
static float32_t lower_bound = 0.0F;
static float32_t Ts = 100.0e-6F;

We define the parameter structure. Each parameter is defined here. 

static PidParams pid_params(Ts, kp, Ti, Td, N, lower_bound, upper_bound);

We define the variable pid which is a Pid object. 

static Pid pid;

In the setup_routine() of the OwnTech Power API, you must initialize the Pid with its parameters.

pid.init(pid_params);

In the loop_critical_task() you can call the method calculateWithReturn() which have two arguments:

  1. the reference
  2. the measure.

Note

Remind that the loop_critical_task() is called at the sampling time you define and must be equal to \(T_s\).

new_command = pid.calculateWithReturn(reference, measurement);

new_command is the result of the pid calculation for one step.

Example

You can find a pid use with the buck voltage mode example which regulates a DC voltage.