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Output Limiting and the Anti-Windup Algorithm The following formula represents the derivative action implemented by the PID VIs, which avoids derivative kick:Ĭontroller output is the summation of the proportional, integral, and derivative action, as shown in the following formula: To avoid derivative kick, you can apply derivative action to the PV only, and not to the error e. These bumps are referred to as derivative kick. Δ T is the sampling time of the controllerĪbrupt changes in SP can generate bumps to the output of the controller as a result of applying derivative action to the error e. The PID VIs use trapezoidal integration to avoid sharp changes in integral action when there is a sudden change in PV or SP, as represented by the following formula: There are several options for discretizing integral action, such as forward difference, backward difference, and trapezoidal approximation, which is also known as Tustin or Bilinear transformation. Integral Action (Trapezoidal Integration) The relationship between controller gain ( K c) and proportional band ( PB) is K c = 100 / PB. The PID VIs express the proportional component in terms of controller gain. Proportional action is the controller gain times the error, as shown in the following formula: K is the index of the sampled signal at time k* t

The following formula represents the current error used in calculating proportional, integral, and derivative action: Refer to the National Instruments website at ni.com for more information about the Control Design and Simulation Module. You do not need the Control Design and Simulation Module to build PID controllers. However, the PID VIs implement PID controllers for you. Note Constructing a simulation diagram like the one in the previous image requires the LabVIEW Control Design and Simulation Module. The following simulation diagram represents the PID implementation provided by the basic PID VIs: The PID Advanced and PID Advanced Autotuning VIs use extended formulas with more advanced optional features. Note The following formulas apply to most VIs on the PID palette. To implement a PID controller, LabVIEW requires the algorithm to sample the input signals and discretize the integral and derivative action. This following sections describe how the basic PID VIs (not including PID Advanced, PID Advanced Autotuning, and other VIs with advanced options) implement the PID algorithm, and the assumptions and transformations necessary to implement the PID controller. Implementing the PID Algorithm with the PID VIs