PID

Block Screenshot

Contents

• Description
• Parameters
• Default properties
• Interfacing function
• Compiled Super Block content
• Examples

Description

This block implements a PID (Proportional-Integral-Differential) controller. It calculates an "error" value U_e as the difference between a measured process variable U_pr and a desired setpoint U_r.

U_e = U_r - U_pr

The purpose is to make the process variable U_p follow the setpoint value U_r. The PID controller is widely used in feedback control of industrial processes.

The PID controller calculation (algorithm) involves three separate parameters; the Proportional Kp, the Integral Ki and Derivative Kd values. These terms describe three basic mathematical functions applied to the error signal Ue. Kp determines the reaction to the current error, Ki determines the reaction based on the sum of recent errors and Kd determines the reaction to the rate at which the error has been changing.

The weighted sum of these three actions is used to adjust the process via a control element such as the position of a control valve or the power supply of a heating element. The basic structure of conventional feedback control systems is shown below:

PID law is a linear combination of an input variable U_p(t), its time integral U_i(t) and its first derivative U_d(t). The control law U_con(t) has the form:

Parameters

• Proportional

  The value of the gain that multiply the error.

  Properties : Type 'vec' of size -1.

• Integral

  The value of the integral time of the error.(1/Integral)

  Properties : Type 'vec' of size -1.

• Derivation

  The value of the derivative time of the error.

  Properties : Type 'vec' of size -1.

Default properties

• always active: no

• direct-feedthrough: no

• zero-crossing: no

• mode: no

• regular inputs:

  - port 1 : size [-1,-2] / type 1

• regular outputs:

  - port 1 : size [-1,-2] / type 1

• number/sizes of activation inputs: 0

• number/sizes of activation outputs: 0

• continuous-time state: no

• discrete-time state: no

• object discrete-time state: no

• name of computational function: csuper

Interfacing function

• SCI/modules/scicos_blocks/macros/Linear/PID.sci

Compiled Super Block content

Examples

Example 1

This example illustrates the usage of PID regulator. It enables you to fit the output signal U_pr(t) to the required signal U_r(t) easily.

In this example the control system is a second-order unity-gain low-pass filter with damping ratio ξ=0.5 and cutoff frequency fc= 100 Hz. Its transfer function H(s) is:

To model this filter we use Continuous transfer function block (CLR) from Continuous time systems Palette.

The PID parameters Kp, Ki and Kd are set to 100, 0.1 and 0.

The scope displays the waveforms of system error U_e (black), reference signal U_r (blue) and process signal U_pr (red). It shows how initially the process signal U_pr(t) does not follow the reference signal U_r(t).

Example 2

Example 3