RQ SSOD PID design tool
This is an application developed in Java to implement the PID design strategy for Send On Delta and RQ event based
sampling, and to simulate the response of the controlled system to setpoint and disturbance changes. The tool allows
to define the desired phase margin and the maximum required Ms (or the minimum required gain margin), and to select
the value of parameter $a=wg*Ti$ with a simple slider, and calculates the controller for that value of $a$ that leads
to the exact required phase margin.
Furthermore, the optimum PID controller (minimum IAE or maximum $K_i$) can be calculated by simply pressing a button.
In addition, if the minimization check is selected, every time a design parameter is changed through its slider (as the phase margin,
, the derivative filter parameter $N$ or the ratio Ti/Td), the optimum controller is automatically calculated. The included output
response simulator allows changing the value of SOD parameter $\delta$ through a slider, making very easy to analyze the effect of
$\delta$ on the behavior and the number of events. The user can select among SSOD and RQ sampling strategies. For the RQ
sampling strategy, besides the value of $\delta$, the hysteresis can also be changed. It also allows to simulate the effect
of a digital controller implementation with the desired sampling period.
The tool simplifies the design of a PID controller that reaches a compromise between control action jumps due to
$\delta$ and performance (IAE). After the desired robustness margins have been defined, with the "MinIAE" check box
selected, and the PID controller type chosen, the user must simply move the $N$ parameter slider till the value of
$\delta u$ is just below the admissible limit, or the value of IAE is the required one, depending on the strategy
that is being applied. If even the lower value of $N=0.1$ results in a too high $\delta u$ then the PI controller type should
be chosen and "MinIAE" unchecked, reducing the value of parameter $a$ to make the response slower and further reduce
the value of $\delta u$ if necessary.
The figures show the main window of the application and the time response simulation window. The Nyquist plot shows the critical points related to the describing functions
of the SSOD and RQ. The encirclement of one of those points by the Nyquist curve implies the appearance of a limit circle if the corresponding event sampling is used.
Robustness margins to oscillations are shown for both SSOD (phase margin) and RQ (gain margin), as well as the percentage of those margins related to the original phase
and gain margins of the design.
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