Classical PID controller. The values for each one of the elements (proportional, integral, derivative and so on) can be changed directly on the screen.

Focusing on the PID structure the next figure and table describe all its elements and what means each one of them.

PID Architecture

ValueDescription
1Measure
2· Invert: Change error sign

· Wrap: Wrap to pi [-π, π]

It is used in some angular variables (radians) for avoiding numerical errors on the –π to π change and keep continuity of the error signal

3Proportional gain
4Discrete filter parameter
5Derivative time parameter
6Derivative gain
7Constant value added to output (Feedforward Control)
8Integral gain
9Inverse integral time parameter
10The maximum value of integral admitted
11Anti-windup parameter
12Output bounds

PID Elements

Output values for PID controller refer to virtual control channels, units must coincide with servo trim configuration settings.

PID diagram represents the following PID model:

ec-c

  • Kp=proportional gain
  • Ti=Integrator time
  • Td=Derivative time
  • N=Derivative filter constant

For the derivation and integration models, Trapezoidal and Backward Euler models have been integrated:

  • Backward Euler:

$$ DF(z) = T_s\frac{z}{z-1} $$

  • Trapezoidal:

$$ DF(z) = \frac{T_s}{2}\frac{z+1}{z-1} $$

$\tau = \frac{T_d}{N}$ where $\tau$ is the time constant on a first order low pass filter (LPF). In Laplace notation:

$$ LPF(s) = \frac{1}{\tau s +1} $$