Step Response Tutorial: Simulating the Step Response of a DM Actuator

This tutorial demonstrates how to set up and analyze the step response of a simplified deformable mirror (DM) actuator model using SPECULA.

Goals: - Simulate the dynamic response of a DM actuator to a step input in closed-loop control - Model the control chain with sample&hold, integrator, and low-pass filter - Visualize the response in real time (no data is saved to disk)

System Overview

The simulated system consists of: - Input generator: a step (or square wave) signal representing the desired actuator command - Sample&Hold: limits the control framerate (e.g., 1 kHz → 1 ms) - Integrator: accumulates the error (controller) - Low-pass filter: models the actuator dynamics, with a configurable cutoff frequency and amplification factor (to simulate resonance)

Block diagram:

[Step Input] → [Sample&Hold] → [Integrator] → [LowPassFilter] → [Output]

YAML Configuration

Create a configuration file, for example params_control_lpf.yml:

main:
  class:             'SimulParams'
  pixel_pupil:       160
  pixel_pitch:       0.05
  total_time:        1.0
  time_step:         0.0001

disturbance:
  class:             'WaveGenerator'
  wave_type:         'SQUARE'
  amp:               [5.0]
  freq:              [50.0]

diff:
  class:             'BaseOperation'
  sub:               True
  inputs:
      in_value1: 'disturbance.output'
      in_value2: 'lowpass.out_comm:-1'

sampHold:
  class:             'WindowedIntegration'
  simul_params_ref:  'main'
  n_elem:            1
  dt:                0.001
  inputs:
      input: 'diff.out_value'

control:
  class:             'Integrator'
  simul_params_ref:  'main'
  delay:             1
  int_gain:          [0.3]
  inputs:
      delta_comm: 'sampHold.output'

lowpass:
  class:             'LowPassFilter'
  simul_params_ref:  'main'
  delay:             0
  cutoff_freq:       [1000]
  amplif_fact:       [3]
  inputs:
      delta_comm: 'control.out_comm'

all_disp:
  class:            'PlotDisplay'
  labels:           ['Input (step)',
                     'Error (diff)',
                     'Integrator command',
                     'Low-pass output']
  inputs:
    value_list: ['disturbance.output',
                 'diff.out_value',
                 'control.out_comm',
                 'lowpass.out_comm']
  yrange:           [-10,10]
  title:            'Step Response'

Block description: - disturbance: generates the input signal (step or square wave) - sampHold: sample&hold to limit the control framerate - control: integrator (controller) - lowpass: low-pass filter modeling the actuator dynamics - all_disp: real-time plot of the main signals

Running the Simulation

To run the simulation, use:

specula params_control_lpf.yml

During the simulation, a real-time plot will show: - Input (step) - Error (diff) - Integrator command - Low-pass filter output (actuator response)

Response Analysis

Observe the actuator response: - Rise time: how quickly the actuator follows the command - Overshoot: possible resonance due to the amplification factor - Steady-state error: difference between input and output after the transition

You can modify the cutoff_freq and amplif_fact parameters in the low-pass filter to see how the actuator performance and resonance change.

Note: In this simulation, data is not saved to disk, only plotted on screen.

Customizations and Experiments

Change the cutoff frequency (cutoff_freq) to simulate faster or slower actuators.
Adjust the integrator gain (int_gain) to see its effect on response speed.
Try different values of amplif_fact to simulate actuator resonance.
Replace the input with other signals (SIN, etc.) to test different responses.

Conclusion

You have simulated and visualized the step response of a DM actuator with digital control and realistic dynamics. This setup is a foundation for testing and optimizing controllers and actuator models in adaptive optics systems.