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lin_method_ilc.py
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lin_method_ilc.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Iterative learning control.
@author: Bikash Adhikari
@date: 25.03.2024
@license: BSD 3-Clause
"""
# %%
import numpy as np
from scipy import linalg, signal
import sys
import random
import tqdm
# from configurations import quantiser_configurations
def get_control(N, N_padding, Xcs, itr, QF_M, L_M, OUT_M, Qstep, Q_levels, Qtype, lvl_dict):
"""
INPUT:
N - Total length of reference/test signal (in sample numbers),
N_padding - Padding length on each end,
Xcs - Reference/test signal
QF_M - Q-filtering matrix
L_M - Learning matrix
OUT_M - Output matrix/Markov parameters/Impulse responses
Qstep - Quantizer step size
Q_levels - Quantizer levels
Qtype - Quantizer type
lvl-dict - Dictionary, where, keys represent the codes and the values represent the
quantized measured(or ideal) levels depending on the Qstep and Range of the quantizer.
OUTPUT:
US - Control (Stacked)
YS - Output
ES - Error
rmsErr - RMS Error
"""
pMatrix = get_periodMatrix(N, N_padding, Xcs)
N_period, T_period = pMatrix.shape # matrix dimensions
US = np.empty([1, itr+1])
YS = np.empty([1, itr+1])
ES = np.empty([1, itr+1])
u_init = Xcs[0]*np.ones(N_period)
# for i in range(T_period):
for i in tqdm.tqdm(range(T_period)):
ref_signal = pMatrix[:,i]
U, Y, E, rE = get_ILC_control(ref_signal, u_init, itr, QF_M, L_M, OUT_M, Qstep, Q_levels, Qtype, lvl_dict)
u_init = U[:,-1] # set initial control for the next period as the optimal control of the last period
# u_init = np.ones(N_period)
# Trim overlaps
U_trim = remove_Overlap(U, N, N_padding)
Y_trim = remove_Overlap(Y, N, N_padding)
E_trim = remove_Overlap(E, N, N_padding)
# Store values
US = np.vstack((US, U_trim))
YS = np.vstack((YS, Y_trim))
ES = np.vstack((ES, E_trim))
# Remove first row
US = np.delete(US, 0,0)
YS = np.delete(YS, 0,0)
ES = np.delete(ES, 0,0)
# RMS Error
rmsErr = []
for i in range(ES.shape[1]):
rmsErr_i = np.sqrt(np.square(ES[:,i]).mean())
rmsErr = np.append(rmsErr, rmsErr_i)
return US
def get_ILC_control(Xcs, u_init, itr, QF_M, L_M, OUT_M, Qstep, Q_levels, Qtype, Mlvl_dict):
"""
INPUTS:
Xcs - Reference / test signal
u_init - Initial control signal
iter - Number of iterations
QF_M - Q-filtering Matrix
L_M - Learning Matrix
OUT_M - Output Matrix
Qstep - Quantization step size
Q_leves - Quantizer leves
Qtype - Quantizer type; Ideal or Nonideal (with INL)
Mlvl_dict - Measured level dictionary
OUTPUTS:
U - Control matrix with values from every iteration
Y - Ouput matrix with values from every iteration
E - Error matrix with values from every iteration
rmsErr - RMSError from every iteration
Note: Only use the value from last iteration for simulation
U, Y, E [:,-1]: Each column represent each iteration.
"""
# Make test signal column vector
Xcs = Xcs.reshape(-1,1)
# Initial Control
# u = np.ones_like(Xcs)
u = u_init.reshape(-1,1)
U = u
# Intial Output
y = OUT_M @ u
Y = y
# Initial Error
e = Xcs - y # reference/test signal - output signal
E = e
# RMS error
rmse = np.sqrt((e**2).mean())
rmsErr = rmse
for i in range(itr):
# Update control using ILC algorithm, Q filter matrix and Learning matrix
u_new = QF_M @(u + L_M @ e)
# Quantize control
q_u_new = direct_quant(u_new, Qstep, Q_levels, Qtype)
# Convert quantized signal to code
Vmin = np.min(Q_levels)
q_u_new_code = gen_code(q_u_new, Qstep, Vmin, Qtype).squeeze()
# Parsing measured levels according to the code
q_u_new_dac = gen_dac_output(q_u_new_code, Mlvl_dict)
q_u = np.array(q_u_new_dac).reshape(-1,1)
# Output
y = OUT_M @ q_u
y = y.reshape(-1,1)
# Error
e = Xcs - y
# Store values
Y = np.hstack((Y, y))
U = np.hstack((U, u_new))
E = np.hstack((E, e))
# Rms Error
rmse = np.sqrt(((e**2).mean()))
rmsErr = np.hstack((rmsErr, rmse))
# Update control
u = u_new.reshape(-1,1)
return U, Y, E, rmsErr
def learning_matrices(len_X, im):
""" Q-filter and Learning matrix generated using results from:
D. A. Bristow, M. Tharayil and A. G. Alleyne, "A survey of iterative learning control,"
in IEEE Control Systems, vol. 26, no. 3, pp. 96-114, June 2006
INPUT:
len_X - Length of reference signal. Q,L,G matrix dimension should match (len_X x len_X)
im - filter's impulse response
OUTPUT:
Q - Q-filtering matrix
L - Learning matrix
G - Plant output matrix
"""
# len_X = len(X) # Length of test signal
h = im[0] # Impulse response
# Tuning matrices
We = np.identity(len_X)
Wf = np.identity(len_X)*1e-4
Wdf = np.identity(len_X)*1e-1
RowVec = np.zeros((1, len_X))
ColumnVec = h[0:len_X]
ColumnVec = np.reshape(ColumnVec, (len(ColumnVec),1))
# Output Matrix
G = linalg.toeplitz(ColumnVec, RowVec)
# Q-filter and Learning Matrices
Subinverse11 = G.transpose() @ We @ G
SubinverseQ = Subinverse11 + Wf + Wdf
SubinverseL = Subinverse11 + Wdf
SubinverseQ = np.linalg.inv(SubinverseQ)
SubinverseL = np.linalg.inv(SubinverseL)
# Q-filter matrix
Q = SubinverseQ @ (G.transpose()@ We @ G + Wdf)
# Learning matrix
L = SubinverseL @ (G.transpose()@We)
# Check if the stability and convergence condition are satisfied
ILCloop = Q - np.matmul(L,G)
eig_ILC, vec_ILC = np.linalg.eig(ILCloop)
eig_ILC_mon, vec_ILC_mon = np.linalg.eig(ILCloop @ ILCloop.transpose())
if max(eig_ILC) <=1:
print('Stablity Condition Satisfied')
if max(eig_ILC_mon) <=1:
print('ILC Monotonic Convergent Condition also Satisfied')
else:
sys.exit('Stability condition not satisfied. Change tuning matrices')
return Q, L, G
def get_periodMatrix(N, N_padding, ref_signal):
N_period = int(N + 2*N_padding) # Total samples in each period (signal length + padding length)
# Reference signal period matrix: Each row contains the reference signal with N_total samples (an arbitrary period)
# N-length signal storage container , first entry
period_matrix = ref_signal[0:N_period]
# Transform to column matrix to store in matrix
period_matrix = period_matrix.reshape(len(period_matrix),1)
# Initial index for second period
index_init = N_period
if len(ref_signal) <= N_period-1:
raise ValueError('Length of reference signal less than the lenght of the period length')
else:
while True:
# indices for each iteration
index1 = int(index_init - N_padding) # inital index for ith period
index2 = int(index1 + N_period) # final index for ith period
# makes the periods of reference signal of same length and store them as matrix
if index2 <= len(ref_signal):
vec_i = np.reshape(ref_signal[index1:index2],(N_period,1))
period_matrix = np.hstack((period_matrix, vec_i))
else:
break
index_init = index2 # update index
return period_matrix
def remove_Overlap(M, N, N_padding):
""" Removes the overlapping due to padding
INPUTS:
M - period Matrix (i.e. the matrix that contains the segments of signals sotred as column vector on matrix M)
N - Length of the segment
N_padding - Padding length
OUTPUT:
M_trim - Trimmed matrix with overlapping due to padding removed
"""
nrows, ncols = M.shape
index1 = int(N_padding/2)
index2 = int(index1 + N + N_padding/2)
M_trim = M[index1:index1 + index2,:]
return M_trim
def direct_quant(Xcs, Qstep, Q_levels, Qtype):
""" Direct quatinzer
INPUT:
Xcs - Reference signal
Qstep - Qantizer step size
Q_levels - Quantizer levels
Qtype - Quantizer type; midread or midrise
OUTPUTS:
q_Xcs - Quantized signal with Qstep, step size
"""
# Range of the quantizer
Vmax = np.max(Q_levels)
Vmin = np.min(Q_levels)
# Select quantizer type
match Qtype:
case "midtread":
q_Xcs = np.floor(Xcs/Qstep +1/2)*Qstep
case "midrise":
q_Xcs = np.floor(Xcs/Qstep )*Qstep +1/2
# Quatizer saturation within its range
np.place(q_Xcs, q_Xcs> Vmax, Vmax)
np.place(q_Xcs, q_Xcs < Vmin, Vmin)
return q_Xcs
def gen_code(q_Xcs, Qstep, Vmin, Qtype):
""" Converter the quantized values to unsigned integers
INPUTS:
q_Xcs - Quantized signal
Qstep - Qantizer step size
Vmin - Quantizer lower range
Qtype - Quantizer type; midread or midrise
OUTPUTS:
q_code - code corresponsing to the quantized values and quantizer levels
"""
match Qtype:
case "midtread":
q_code = q_Xcs/Qstep - np.floor(Vmin/Qstep)
case "midrise":
q_code = q_Xcs/Qstep - np.floor(Vmin/Qstep) - 1/2
return q_code.astype(int)
def gen_dac_output(q_codes, ML_dict):
"""
INPUTS:
q_codes - quantized signal in codes
ML_dict - measured levels corresponding to the code, LUT
OUTPUTS:
q_dac - Emulated DAC output
"""
q_dac = []
for i in q_codes:
q_dac_i = ML_dict[i] # assing value to the code
q_dac.append(q_dac_i)
return q_dac
def generate_ML(Nb, Qstep, Q_levels):
# Generate random INL for the simulation
level_codes = np.arange(0, 2**Nb,1) # Levels: 0, 1, 2, .... 2^(Nb)
inl = []
for _ in range(2**Nb):
inl.append(Qstep*random.randint(-10,10))
inl = np.array(inl)
inl[0:2] = 0
inl[-2:] = 0
ml = Q_levels + inl
ML_dict = dict(zip(level_codes, ml))
return ML_dict