second simulation breaks the loop at the plant input, and perturbs the plant with sine and
step signals. The tuner takes the difference between the two simulated responses, which
removes the effect of any disturbances in the model. The tuner then uses the resulting
data to estimate the plant frequency response. Finally, it uses the estimated frequency
response to compute PID gains.
When you open the Frequency Response Based PID Tuner, it reads parameters from
the PID Controller block to determine the structure of your PID controller. These
parameters include:
- PID Controller Type (P, I, PI, PID etc.)
- PID Controller Form (Parallel, Ideal)
- Integrator Method, if applicable (Forward Euler, Trapezoidal etc.)
- Derivative Filter Method, if applicable (Forward Euler, Trapezoidal etc.)
- Sample Time, if applicable
Specify Experiment Settings
Before tuning, specify parameters of the experiment the tuner performs to estimate the
frequency response of the plant.
Start time is the time, in seconds, at which the tuner begins applying the perturbation
signals to the plant. Choose a start time at which the plant is at the nominal operating
point you want to use for tuning. For this example, the buck converter has an initial
transient that falls off by 0.002 seconds. Therefore, enter 0.002 for Start Time.
Specify the Duration of the perturbation experiment. A conservative estimate for the
duration of the experiment is 100 divided by the target bandwidth. The target bandwidth
is approximately 2/τ, where τ is the desired rise time. For this example, the desired rise
time is 250e-6 seconds which results in a target bandwidth of 8000 radians per second. In
this example a conservative estimate for the duration would then be 100/8000 or 0.0125
seconds. Choose 0.0125 seconds for the Duration.
During the experiment, the tuner injects sinusoidal signals into the plant at four
frequencies, [1/3, 1, 3, 10] , where is the target bandwidth you specify for tuning.
Specify the amplitudes of the injected sine waves in the Sine Amplitudes field.
Choose amplitudes which have magnitudes above the noise floor of the system and will
not saturate the system. For this example there is no noise in the system to consider.
However, the controller output (duty cycle of the PWM) is limited to [0 1] and the nominal
Design PID Controller Using Plant Frequency Response Near Bandwidth