This information is part of the Modelica Standard Library maintained by the Modelica Association.

This is the text-book version of a PID-controller. For a more practically useful PID-controller, use block LimPID.

The PID block can be initialized in different ways controlled by parameter initType. The possible values of initType are defined in Modelica.Blocks.Types.InitPID. This type is identical to Types.Init, with the only exception that the additional option DoNotUse_InitialIntegratorState is added for backward compatibility reasons (= integrator is initialized with InitialState whereas differential part is initialized with NoInit which was the initialization in version 2.2 of the Modelica standard library).

Based on the setting of initType, the integrator (I) and derivative (D) blocks inside the PID controller are initialized according to the following table:

initType	I.initType	D.initType
NoInit	NoInit	NoInit
SteadyState	SteadyState	SteadyState
InitialState	InitialState	InitialState
InitialOutput and initial equation: y = y_start	NoInit	SteadyState
DoNotUse_InitialIntegratorState	InitialState	NoInit

In many cases, the most useful initial condition is SteadyState because initial transients are then no longer present. If initType = InitPID.SteadyState, then in some cases difficulties might occur. The reason is the equation of the integrator:

   der(y) = k*u;

The steady state equation "der(x)=0" leads to the condition that the input u to the integrator is zero. If the input u is already (directly or indirectly) defined by another initial condition, then the initialization problem is singular (has none or infinitely many solutions). This situation occurs often for mechanical systems, where, e.g., u = desiredSpeed - measuredSpeed and since speed is both a state and a derivative, it is natural to initialize it with zero. As sketched this is, however, not possible. The solution is to not initialize u or the variable that is used to compute u by an algebraic equation.

k	Value: 1 Type: Real Description: Gain
Ti	Value: Type: Time (s) Description: Time Constant of Integrator
Td	Value: Type: Time (s) Description: Time Constant of Derivative block
Nd	Value: 10 Type: Real Description: The higher Nd, the more ideal the derivative block
initType	Value: Modelica.Blocks.Types.InitPID.DoNotUse_InitialIntegratorState Type: InitPID Description: Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output)
xi_start	Value: 0 Type: Real Description: Initial or guess value for integrator output (= integrator state)
xd_start	Value: 0 Type: Real Description: Initial or guess value for state of derivative block
y_start	Value: 0 Type: Real Description: Initial value of output