PD Controller

Operator Menu Location: Generic Hardware Operators -> Controller Blocks

Operator Bitmap:

Functional Description:
The PD Controller block implements the position form of a Proportional-Derivative control algorithm . It computes a control signal M, as the sum of proportional, integral (reset), and derivative (rate) control modes:

Each mode is based on measurements (samples) of an error signal E. For direct-acting control, this error signal is defined as
E = PV - SP,

where PV is the process variable and SP is the set-point. For reverse-acting control, the error is defined as
E = SP - PV.

The direct/reverse acting attribute of a PD controller refers to the relative direction of movement of the process variable and controller output. Under a direct acting configuration, an increase in the process variable results in an increase in the controller output. Under a reverse acting configuration, an increase in the process variable results in a decrease in controller output. The proper setting depends upon the process itself. In most processes, the controller should be set to reverse acting. (Hence, the operator defaults to reverse acting.)
The proportional mode term, , is calculated as the product of the proportional gain, , and the error term E(t),

The derivative mode term, , is obtained from

where is the derivative time, expressed in minutes. With this definition, a change in the process set-point can cause undesirable pulses in the derivative mode term. These undesirable pulses, known as derivative kick, can also result from discretization effects and from the noise-amplification effect of differentiation. Derivative kick can be avoided by having the derivative mode act on the process variable, rather than on the error. To avoid derivative kick is calculated from

where (delta)PV is the process variable change from one sample to the next. For direct acting processes, we have
_(delta)_PV(t) = PV(t) - PV(t-(delta)t)
and for reverse acting processes, we have
(delta)PV(t) = -PV(t) + PV(t(delta)-t)

The parameter before B sub D (z in this discussion) in the equations above acts as a noise filter. Its reciprocal, 1/z, is called the "dynamic gain limit" and corresponds to the maximum amplification of the error signal. By default, the operator is configured to avoid derivative kick. And, the default value of the filter parameter is set to z=1.

User-Defined Properties:
Object Name. A string label that identifies the operator

Initial Condition. The output value at startup, i.e., M(0)

Minimum Output. The minimum output value

Maximum Output. The maximum output value

Direct Acting. A boolean property that governs the relative direction of movement of the process variable and controller output. When the property is checked, an increase in the process variable results in an increase in the controller output. When it is not checked, an increase in the process variable results in a decrease in controller output. By default, this property is left unchecked (in most applications, a PD controller should be reverse acting.)

Derivative on Measure. A boolean property that governs the computation of the derivative-mode term. When this property is checked, the derivative mode term is based on the process variable; when it is not checked, it is based on the error. The latter case may result in derivative kick when the set-point is modified, or when the operator switches between automatic and manual modes. By default, this property is checked to eliminate derivative kick and to limit the noise amplification effect of differentiation.

Filter Parameter, A scalar parameter used when the 'Derivative on Measure' property is checked. It serves to limit the effects of noise and discretization on the derivative-mode term.

Comments:
•The rate time ( ) input is measured in minutes
•The minimum proportional gain ( ) input is 0.001 (if a smaller value is present, 0.001 will be used as the gain in the computation of the output signal.)

See Also:
PID Controller, PI Controller, PID Controller with External Feedback, Lead-Lag Controller