RST and ILC design for I/B-Loop
The examples here will consider designing the RST and ILC controllers for the current loop. A design for the field loop will be very similar. For simplicity, the examples will consider the desired control parameters taken from the default function (see API Reference):
>>> import pyfresco.obcd as cd >>> device = 'RFNA.866.01.ETH2' >>> user_pars_ib = cd.get_default_i(device) >>> user_pars_ib <pyfresco.obcd.props.UiParams object at 0x7f1b94368160> >>> vars(user_pars_ib) {'des_bw': 133.3333334, 'des_z': 0.8, 'des_mm': 0.5, 'n_integrators': 2, 'ref_delay': 0, 'opt_method': 'Hinf', 'n_r': 6, 'n_s': 6, 'n_t': 6, 'n_ilc': 5, 'n_q': 5, 'q_bw': 400.0, 'control_mode': 'I', 'test_select': False, 'noise_rej': [], 'debug': False} >>> fgc_ib = cd.FgcProperties.from_fgc_ib(user_pars_ib, device) >>> fgc_ib <pyfresco.obcd.props.FgcProperties object at 0x7f1b943684a8> >>> vars(fgc_ib) {'LOAD.OHMS_SER': 9.9999997e-06, 'LOAD.OHMS_MAG': 0.13600001, 'LOAD.OHMS_PAR': 100000000.0, 'LOAD.HENRYS': 0.0063999998, 'LOAD.GAUSS_PER_AMP': 1.0, 'VS.SIM.BANDWIDTH': 1000.0, 'VS.SIM.Z': 0.69999999, 'VS.ACTUATION': 'VOLTAGE_REF', 'VS.FIRING.DELAY': 0.00166667, 'VS.ACT_DELAY_ITERS': 1.5, 'REG.I.PERIOD_ITERS': 5.0, 'FGC.ITER_PERIOD': 9.9999997e-05, 'REG.I.INTERNAL.PURE_DELAY_PERIODS': 0.0, 'MEAS.I.DELAY_ITERS': 0.51999998, 'MEAS.V.DELAY_ITERS': 0.51999998, 'REG.I.EXTERNAL.MEAS_SELECT': 'UNFILTERED', 'REG.I.EXTERNAL.Z': 0.80000001, 'REG.I.EXTERNAL.MOD_MARGIN': 0.5, 'MEAS.I.FIR_LENGTHS': [0, 0]}
Model-based design (I/B)
The model-based design uses the FGC properties to design a controller. It is thus imperative that the correct load properties are set in the FGC. This method can be used in cases where a frequency response measurement cannot be obtained from a particular power converter. The model-based design can be completed by simply calling the following functions:
>>> X = cd.OptimizeIB(fgc_ib, user_pars_ib) >>> opt_result, df_sens, margins = X.model_opt() >>> vars(opt_result) {'R': array([10.58623286, -5.57877783, -6.82957127, -3.67676923, 5.35465179, 0.31557969]), 'S': array([ 1. , -0.60378036, -0.81877469, -0.21697569, 0.30539692, 0.33413383]), 'T': array([ 2.82797628, -0.6342463 , -0.39158306, -1.2070911 , -0.47758528, 0.05387546]), 'dtrack': 3.4554860956062403, 'L': array([ 0.15354691, -0.43997275, 0.60930577, -0.46870985, 2.23952406, -5.02945471, 1.24076391, 4.6586344 , -3.39532177, 2.07031252, -0.64104597]), 'Q': array([ 5.25225103e-04, -1.24165523e-03, 6.52180501e-03, 1.08316106e-02, 1.67918023e-01, 6.30889983e-01, 1.67918023e-01, 1.08316106e-02, 6.52180501e-03, -1.24165523e-03, 5.25225103e-04])}
The opt_result object contains both the RST and ILC filter parameters (along with
REG.I.EXTERNAL.TRACK_DELAY_PERIODS
given by the parameter dtrack). The results from the optimization problem can
then be sent to the FGC as follows:
>>> cd.FgcProperties.to_fgc_ib(opt_result, user_pars_ib, device)
The output dataframe df_sens contains the closed-loop sensitivity functions, and is discussed in
Sensitivity functions. Finally, margins contains the calculated robustness
margins (in dictionary format) of the closed-loop system: modulus_margin, gain_margin,
phase_margin and delay_margin.
Data-driven design (I/B)
To perform a data-driven design, the frequency response from V_REF to I_MEAS is needed (or V_REF to B_MEAS for field control). Let us suppose that a PRBS or sine-fit experiment was performed with the following frequency response
>>> df_freq f gain phase 0 1.220852 16.797757 -20.015512 1 2.441704 15.510021 -36.172323 2 3.662556 13.963785 -47.810938 3 4.883409 12.442825 -56.015474 4 6.104261 11.044407 -61.922417 .. ... ... ...
The data-driven design can then be completed by simply calling the following functions:
>>> X = cd.OptimizeIB(fgc_ib, user_pars_ib) >>> opt_result, df_sens, margins = X.data_opt(df_freq) >>> vars(opt_result) {'R': array([10.82914723, -6.04830058, -6.37072024, -4.0319094 , 5.5032835 , 0.30051736]), 'S': array([ 1. , -0.60540888, -0.81165273, -0.21422895, 0.28505159, 0.34623896]), 'T': array([ 2.86164262, -0.66994455, -0.34357477, -1.21909757, -0.49924941, 0.05224155]), 'dtrack': 3.411909048893395, 'L': array([ 0.75694795, -1.38435525, 1.11347752, -0.59444607, 2.40050818, -5.41419615, 1.86901783, 4.13754392, -4.15915052, 4.43455996, -2.29519351]), 'Q': array([ 0.00076679, -0.0014831 , 0.00658921, 0.01081398, 0.16783134, 0.63096355, 0.16783134, 0.01081398, 0.00658921, -0.0014831 , 0.00076679])}