WOLFRAM SYSTEMMODELER

PID

PID-controller in additive description form

Diagram

Wolfram Language

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SystemModel["Modelica.Blocks.Continuous.PID"]
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Information

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.

Connectors (2)

u

Type: RealInput

Description: Connector of Real input signal

y

Type: RealOutput

Description: Connector of Real output signal

Parameters (8)

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 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

Components (5)

P

Type: Gain

Description: Proportional part of PID controller

I

Type: Integrator

Description: Integral part of PID controller

D

Type: Derivative

Description: Derivative part of PID controller

Gain

Type: Gain

Description: Gain of PID controller

Add

Type: Add3

Description: