Henrik Manum, student, NTNU Extensions of Skogestad’s SIMC tuning rules to oscillatory and unstable processes Henrik Manum, student, NTNU

Project goals Extend the SIMC-rules to oscillatory and unstable processes Reduce the model at hand to a first or second order plus delay model can use existing SIMC-rules on the reduced model Derive new rules based on the given model

Reminder of the SIMC PID tuning rules Assume we have a model on one of the following forms: SIMC-PID controller settings: Fast and robust

Processes covered Stable process with pair of complex poles Unstable process with single real RHP pole

Stable process with pair of complex poles Divide the processes into three parts Category A Pure 2nd order underdamped system Category B Damped oscillations, but a clear peak in the frequency domain Category C Peak less than steady state gain Main focus today

Category B Resonant peak, asymptotically: Phase, empirical, from Bode-plot Conservative for all frequencies Most likely too complicated, but will use this as a starting-point.

Category B Justification for gain-approximation Peak in gain for pure 2nd order under-damped process:

Category B

Category B So, we use the maximum gain to stay safe in gain, and we use the empirical phase-approximation to get a model on the form with the approximations given in the previous slides

Category B Direct synthesis of controller for the process (for setpoints) Pure I-controller

Category B Performance and robustness evaluation of the resulting I-controller Want to solve this optimization problem for a PI-controller and compare the resulting controller to our I-controller

Category B Naive solution to the optimization problem:

Category B Our I-controller

Category B Our I-controller

Category B Pros and cons with this method of controller evaluation Difficult to find a solution SIMULINK model often diverges The problem is most likely non-convex Good graphical representation of trade-off between IAE and TV Further work: Look at method by Kristiansson and Lennartson. Frequency based approach Broader range of input-signals Probably easier to use in practice

The remaining processes Category C: Same procedure as category B, but with I derived a 1st order model with a resulting PI-controller Categroy A: Pure oscillatory. Based on work done by prof. Skogestad, compared with method from literature Unstable process: Reviewed work by prof. Skogestad and compared to a method found in literature PLEASE CONSULT THE REPORT IF YOU HAVE INTEREST

Summary The goal of extending the SIMC rules to oscillatory and unstable processes has not been achieved, but we are closer to the goal than when we started The author has learned a lot, including: Frequency analysis Robustness and performance measures in frequency domain Properties of linear models in frequency domain in general Optimization used in practice Time domain analysis Experience with Matlab on control problems

References SIMC-rules Optimal controller For more references see the report

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