blockPI

Proportional-Integral controller

Extends from Interfaces.SISO (Single Input Single Output continuous control block).

Information

This blocks defines the transfer function between the input u and the output y as PI system:

              1
y = k * (1 + ---) * u
             T*s
        T*s + 1
  = k * ------- * u
          T*s

If you would like to be able to change easily between different transfer functions (FirstOrder, SecondOrder, ... ) by changing parameters, use the general model class TransferFunction instead and model a PI SISO system with parameters
b = {k*T, k}, a = {T, 0}.

Example:

   parameter: k = 0.3,  T = 0.4

   results in:
               0.4 s + 1
      y = 0.3 ----------- * u
                 0.4 s

It might be difficult to initialize the PI component in steady state due to the integrator part. This is discussed in the description of package Continuous.

Parameters

Type	Name	Default	Description
Real	k	1	Gain
SI.Time	T		Time Constant (T>0 required)
Initialization
Init	initType	Init.NoInit	Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output)
Real	x_start	0	Initial or guess value of state
Real	y_start	0	Initial value of output

Connectors

Type	Name	Default	Description
RealInput	u (from SISO)		Connector of Real input signal
RealOutput	y (from SISO)		Connector of Real output signal

Components

Type	Name	Default	Description
Real	x		State of block