Frequency-Response Based Tuning
Frequency Response Based PID Tuner simulates the model to estimate the plant
frequency responses at a few frequencies near the control bandwidth. It then uses the
estimated frequency response to tune the gains in your PID Controller. This tuner is a
useful alternative when PID Tuner cannot linearize the plant at the operating point you
want to use for tuning.Frequency Response Based PID Tuner can tune the P, I, D, and N parameters in PID
Controller and PID Controller (2DOF) blocks in both continuous time and discrete time.
For PID Controller (2DOF) blocks, the tuner does not tune the setpoint weights b and c.How Frequency Response Based PID Tuner Works
Like the interactive PID Tuner, the Frequency Response Based PID Tuner considers
the plant to be all blocks in the loop between the PID Controller block output and input.
The Frequency Response Based PID Tuner performs a perturbation experiment to
estimate the open-loop frequency response of the plant. To do so, the tuner performs the
following steps:(^1) Breaks the feedback loop at the controller output and simulates the model, applying
perturbation signals to the plant. The perturbations include sinusoidal signals at
frequencies [1/3,1,3,10]ωc , where ωc is the target bandwidth you specify for tuning.
If the plant is asymptotically stable, the applied signal also includes a step
perturbation.
(^2) Measures the response to the perturbation at the controller input.
(^3) Uses the resulting data to estimate the plant frequency response at the four
frequencies. For asymptotically stable plants, the tuner also uses the response to the
step perturbation to estimate the plant DC gain.
(^4) Uses the estimated frequency response to compute PID gains that balance
performance and robustness.
If your model includes disturbances, the tuner can run two simulations: a simulation
without perturbation to get a baseline response, and a simulation with the perturbations
applied to the plant. The tuner then uses the difference between the two responses to
remove the effects of disturbances in the model. In this case, the estimated frequency
response used for tuning is based on this disturbance-free response.