Ahmed-ElTahan/Deterministic-Indirect-Self-Tuning-Regulator-One-Degree-Controller
It's intended to apply the self-tuning regulator for a given system
such as
y z^(-d) Bsys
Gp = ------ = ----------------------
u Asys
the controller is given in the form of
u S
Gc = ------ = -------
err R
the closed loop transfer function
y z^(-d)BsysS z^(-d)BsysS z^(-d)BsysS
------ = ---------------------------------- = ------------------- = ------------------------
uc AsysR + z^(-d)BsysS Am A0 alpha
where
-- y : output of the system
-- u : control action (input to the system)
-- uc : required output (closed loop input-reference, command signal)
-- err = error between the required and the output --> = uc - y
-- Asys = 1 + a_1 z^-1 + a_2 z^-1 + ... + a_na z^(-na)
-- Bsys = b_0 + b_1 z^-1 + b_2 z^-1 + ... + b_nb z^(-nb)
-- R = 1 + r_1 z^-1 + r_2 z^-1 + ... + r_nr z^(-nr) --> [1, r_1, r_2, r_3, ..., r_nr]
-- S = s_0 + s_1 z^-1 + s_2 z^-1 + ... + s_ns z^(-ns) --> [s_0, s_1, s _2, s_3, ..., s_ns]
-- d : delay in the system. Notice that this form of the Diaphontaing solution
is available for systems with d>=1
-- Am = required polynomial of the model = 1+m_1 z^-1 + m_2 z^-1 + ... + m_nm z^(-m_nm)
-- A0 = observer polynomail for compensation of the order = 1 + o_1 z^-1 + o_2 z^-1 + ... + o_no z^(-no)
-- alpha:required characteristic polynomial = Am A0 = 1 + alpha1 z^-1 + alpha2 z^-1 + ... + alpha_(nalpha z)^(-nalpha)
Steps of solution:
1- initialization of the some parameters (theta0, P, Asys, Bsys, S, R, T, y, u, err, dc_gain).
2- assume at first the controller is unity. Get u, y of the system
3- RLS and get A, B estimated for the system.
4- Solve the Diophantine equation using A, B and the specified "alpha = AmA0" and get S, R of the controller.
5- find "u" due to this new controller and then y.
6- repeat from 3 till the system converges.
Function Inputs and Outputs
Inputs
uc: command signal (column vector)
Asys = [1, a_1, a_2, a_3, ..., a_na] ----> size(1, na)
Bsys = [b_0, b_1, b _2, b_3, ..., a_nb]----> size(1, nb)
d : delay in the system (d>=1)
Ts : sample time (sec.)
Am = [1, m_1, m_2, m_3, ..., m_nm]---> size(1, nm)
A0 = [1, o_1, o_2, o_3, ..., o_no]---> size(1, no)
alpha : [1, alpha_1, alpha _2, alpha_3, ..., alpha_nalpha] ----> size(1, nalpha) row vector
Outputs
Theta_final : final estimated parameters
Gz_estm : estimated pulse transfer function
Gc = the controller by Diophantine equation = S/R
Gcl = closed loop transfer function
here we may input the signal uc by dividing it by the dc gain in order to
force the output to follow the input in magnitude
인용 양식
Ahmed ElTahan (2024). Ahmed-ElTahan/Deterministic-Indirect-Self-Tuning-Regulator-One-Degree-Controller (https://github.com/Ahmed-ElTahan/Deterministic-Indirect-Self-Tuning-Regulator-One-Degree-Controller), GitHub. 검색됨 .
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