second_order_time_domain_sys_ID

Summary

Python and MATLAB codebase for performing second-order system identification from time-domain data of a decreasing step response. Both discrete and continuous time estimation methods are available. Uncertainties given at the 95% confidence level. Code was originally developed to characterize dynamics of pressure sensor apparatuses through decreasing step response testing.

Dependencies

Python

1. functions.py
2. matplotlib.pyplot
3. matplotlib.SpanSelector
4. numpy
5. pandas
6. scipy

MATLAB

1. Control Systems Toolbox

Order of Use of Code

1. csv_crop_prgrm.py (crop time-domain data to obtain portion of response that carries the dynamic chracteristics.)

Discrete-Time OLS Identification

2. second_order_approx_w_LS.py or 2_order_LS_w_2_zero.py (Perform OLS fit of discrete-time 2nd order model to cropped time-domain data considering either a single zero or two zeroes, outputs estimated parameters.)
3. ct_param_est_from_dt_param_est.m or ct_param_est_from_dt_param_est_2_zeroes.m (Convert discrete-time transfer function estimated in 2. to continuous-time, also obtain step response data of simulated transfer function for comparison to experimental data. Use for either one or two zeroes.)
4. lsim_prgrm.m (Obtain simulation data of the response of the estimated model to the same input applied to the real system.)

Continuous-Time Identification

2. second_order_approx_Tr_and_OS.py (Estimate natural frequency and damping ratio from response charactersitics obtained from cropped time-domain data.)
3. second_order_response_from_dr_and_wn.m (Calculating general second-order TF parameters from estimated nat. freq and damping ratio. Also obtaining frequency response data.)
4. lsim_prgrm.m (Obtain simulation data of the response of the estimated model to the same input applied to the real system.)