PID

Description

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

The PID block can be initialized in differentways controlled by parameter initType. The possiblevalues of initType are defined inModelica.Blocks.Types.InitPID.This type is identical toTypes.Init,with the only exception that the additional optionDoNotUse_InitialIntegratorState is added forbackward compatibility reasons (= integrator is initialized withInitialState whereas differential part is initialized withNoInit which was the initialization in version 2.2 of the Modelicastandard 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:

In many cases, the most useful initial condition isSteadyState because initial transients are then no longerpresent. If initType = InitPID.SteadyState, then in somecases difficulties might occur. The reason is theequation of the integrator:

   der(y) = k*u;

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