ContinuousLibrary of continuous control blocks with internal states 
Output the integral of the input signal with optional reset 

Integrator with limited value of the output and optional reset 

Approximated derivative block 

First order transfer function block (= 1 pole) 

Second order transfer function block (= 2 poles) 

ProportionalIntegral controller 

PIDcontroller in additive description form 

P, PI, PD, and PID controller with limited output, antiwindup compensation, setpoint weighting and optional feedforward 

Linear transfer function 

Linear state space system 

Derivative of input (= analytic differentiations) 

Output the input signal filtered with a low pass Butterworth filter of any order 

Output the input signal filtered with an nth order filter with critical damping 

Continuous low pass, high pass, band pass or band stop IIRfilter of type CriticalDamping, Bessel, Butterworth or ChebyshevI 

Internal utility functions and blocks that should not be directly utilized by the user 
This information is part of the Modelica Standard Library maintained by the Modelica Association.
This package contains basic continuous input/output blocks described by differential equations.
All blocks of this package can be initialized in different ways controlled by parameter initType. The possible values of initType are defined in Modelica.Blocks.Types.Init:
Name  Description 
Init.NoInit  no initialization (start values are used as guess values with fixed=false) 
Init.SteadyState  steady state initialization (derivatives of states are zero) 
Init.InitialState  Initialization with initial states 
Init.InitialOutput  Initialization with initial outputs (and steady state of the states if possible) 
For backward compatibility reasons the default of all blocks is Init.NoInit, with the exception of Integrator and LimIntegrator where the default is Init.InitialState (this was the initialization defined in version 2.2 of the Modelica standard library).
In many cases, the most useful initial condition is Init.SteadyState because initial transients are then no longer present. The drawback is that in combination with a nonlinear plant, nonlinear algebraic equations occur that might be difficult to solve if appropriate guess values for the iteration variables are not provided (i.e., start values with fixed=false). However, it is often already useful to just initialize the linear blocks from the Continuous blocks library in SteadyState. This is uncritical, because only linear algebraic equations occur. If Init.NoInit is set, then the start values for the states are interpreted as guess values and are propagated to the states with fixed=false.
Note, initialization with Init.SteadyState is usually difficult for a block that contains an integrator (Integrator, LimIntegrator, PI, PID, LimPID). This is due to the basic equation of an integrator:
initial equation der(y) = 0; // Init.SteadyState equation der(y) = k*u;
The steady state equation leads to the condition that the input 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 always defined by Init.InitialState or Init.SteadyState initialization.
In such a case, Init.NoInit has to be selected for the integrator and an additional initial equation has to be added to the system to which the integrator is connected. E.g., useful initial conditions for a 1dim. rotational inertia controlled by a PI controller are that angle, speed, and acceleration of the inertia are zero.