Code covered by the BSD License
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[param]=db2s(input)
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[param]=db2w(input)
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[param]=db3s(input)
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[param]=db3w(input)
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[param]=mv2(input)
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[param]=pp2b_1(input)
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[param]=pp2b_2(input)
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[param]=pp2c2dof(input)
[param]=pp2c2dof(input)
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[param]=pp2chp(input)
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[param]=pp2chp(input)
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[param]=pp3c2dof(input)
[param]=pp3c2dof(input)
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[param]=pp3chp(input)
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[param]=zn2ast(input)
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[param]=zn2ast(input)
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[param]=zn2pd(input)
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[param]=zn2tak(input)
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[param]=zn3pd(input)
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[param]=zn3tak(input)
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[q]=zn2fpd(input)
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[q]=zn3fpd(input)
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[qp]=ba2(input)
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[qp]=da2(input)
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[qp]=pp2a_1(input)
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[qp]=pp2a_2(input)
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[qp]=zn2br(input)
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[qp]=zn2fd(input)
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[qp]=zn2fr(input)
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[qp]=zn2pi(input)
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[qp]=zn2tr(input)
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[qp]=zn3br(input)
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[qp]=zn3fd(input)
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[qp]=zn3fr(input)
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[qp]=zn3pi(input)
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[qp]=zn3tr(input)
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[sys,x0,str,ts]=sid(t,x,u,fla...
Discrete model identification function.
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scast(t,x,u,flag,T0,alfa,beta...
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scfpd(t,x,u,flag,T0)
PID controller based on forward rectangular method of discretization
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scqp(t,x,u,flag,T0)
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scrqp(t,x,u,flag,T0)
RQP feedforward feedback controller
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scrqp(t,x,u,flag,T0,nr,nq,np)
FBFW feedforward feedback controller
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slblocks
% Name of the subsystem which will show up in the Simulink Blocksets
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ultim(B,A,T0,trace)
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circuit_rtw
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stcsl_rtw
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View all files
from
STCSL - RTW version
by Petr Chalupa
Self-Tuning Controllers Simulink Library - Real Time Workshop version.
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| [param]=pp3chp(input)
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function [param]=pp3chp(input)
% [param]=pp3chp(input)
% Pole placement controller for 3rd order processes.
% This function computes parameters of the controller (r0, r1, q0, q1, q2, p0, p1, p2).
% The dynamic behavoiour of the closed-loop is defined by coefficients of
% characteristic polynomial D = d0 + d1*z^-1 + d2*z^-2 + d3*z^-3.
% Output of the controller is calculated follows:
%
% r0 + r1*z^-1 q0 + q1*z^-1 + q2*z^-2
% U(z^-1) = ------------------------ * W(z^-1) - ------------------------ * Y(z^-1)
% p0 + p1*z^-1 + p2*z^-2 p0 + p1*z^-1 + p2*z^-2
%
% Transfer function of the controlled system is:
%
% b1*z^-1 + b2*z^-2 + b3*z^-3
% Gs(z^-1) = ---------------------------------
% 1 + a1*z^-1 + a2*z^-2 + a3*z^-3
%
% Input:
% input(1:6) ... [a1 b1 a2 b2 a3 b3]
% input(7) ... type of reference signal (1-step, 2-ramp, 3-sin)
% input(8) ... frequency [Hz] (used if reference signal is sin wave)
% input(9) ... sample time (used if reference signal is sin wave)
% input(10:15) ... [d0 d1 d2 d3] coefficients of characteristic polynomial
% d0 is required, d1, d2 and d3 are voluntary
% Output: param ... controller parameters [r0; r1; q0; q1; q2; p0; p1; p2];
a1 = input(1);
b1 = input(2);
a2 = input(3);
b2 = input(4);
a3 = input(5);
b3 = input(6);
rs_type = input(7);
rs_freq = input(8);
T0 = input(9);
d0 = input(10);
d1 = 0;
d2 = 0;
d3 = 0;
d4 = 0;
d5 = 0;
if length(input) > 10,
d1 = input(11);
if length(input) > 11,
d2 = input(12);
if length(input) > 12,
d3 = input(13);
if length(input) > 13,
d2 = input(14);
if length(input) > 14,
d3 = input(15);
end;
end;
end;
end;
end;
% FBFW controller: Y=BR/(AP+BQ)*W
% conditions: 1) AP+BQ=D
% 2) BR+FS=D where W=H/F and S is any polynomial
% 1st condition:
% A = 1 + a1*z^-1 + a2*z^-2 + a3*z^-3 B = b1*z^-1 + b2*z^-2 + b3*z^-3
% P = p0 + p1*z^-1 + p2*z^-2 Q = q0 + q1*z^-1 + q2*z^-2
% system of linear equations:
% [ 1 0 0 0 0 0] [p0] [d0]
% [a1 1 0 b1 0 0] [p1] [d1]
% [a2 a1 1 b2 b1 0] [p2] [d2]
% [a3 a2 a1 b3 b2 b1] * [q0] = [d3]
% [ 0 a3 a2 0 b3 b2] [q1] [d4]
% [ 0 0 a3 0 0 b3] [q2] [d5]
p0 = d0;
p1 = (-2*d0*a3*b2*b3*a1*b1-b1*d2*b3*a2*b2+2*d1*b1*a3*b2*b3-d0*b1*a3*a2*b2^2+d0*b3*b2*a2^2*b1-d0*b3*a2*a1*b2^2 ...
+d1*b3^3-d1*a3*b2^3-d0*a1*b3^3+b1^2*d3*b3*a2-b1^2*d3*a3*b2+b1*d2*a3*b2^2-b1^2*d2*b3*a3+b1*d2*b3^2*a1 ...
+d1*b2^2*b3*a2-d1*b3^2*a2*b1-d1*b2*b3^2*a1+d0*b1^2*a3^2*b2-b1^3*d5*a2+d0*a3*a1*b2^3-b1*d5*b2^2+b1^2*d5*b3 ...
+d0*b1*b3^2*a3+b1^3*d4*a3+d0*b3^2*a1^2*b2-b1*d3*b3^2+b1^2*d5*a1*b2-b1^2*d4*b3*a1+b1*d4*b3*b2)/ ...
(-a3*b2^3+b2^2*a3*a1*b1+b2^2*b3*a2-b1^2*a3*a2*b2+3*b1*a3*b2*b3-b2*b3^2*a1-b2*b3*a2*a1*b1+a3^2*b1^3 ...
-2*a3*a1*b1^2*b3+b3^2*a1^2*b1+b3^3+b1^2*a2^2*b3-2*b3^2*a2*b1);
p2 = (-b3^3*d0*a2-d5*b2^3-d5*b1^2*a2*b2+d5*a1*b1*b2^2-d5*b1^2*a1*b3+2*d5*b3*b1*b2-b3*d4*a1*b1*b2 ...
+b3*d4*b1^2*a2-b3*d3*b1^2*a3+b3^2*d3*a1*b1-b3^2*d2*a2*b1-b3*d1*a3*b2^2+b3^2*d1*a3*b1+b3^2*d1*a2*b2 ...
+b3*d2*b1*a3*b2+b3*d0*a3^2*b1^2+b3^3*d2-b3*d0*a3*b2*a2*b1+b3*d0*b2^2*a1*a3+b3^2*d0*a2^2*b1-2*b3^2*d0*a3*a1*b1 ...
-b3^2*d0*b2*a2*a1+b3^2*d0*a3*b2-b3^2*d4*b1-b3^2*d3*b2-b3^3*d1*a1+b3^3*d0*a1^2+d5*b1^3*a3+b3*d4*b2^2)/ ...
(-a3*b2^3+b2^2*a3*a1*b1+b2^2*b3*a2-b1^2*a3*a2*b2+3*b1*a3*b2*b3-b2*b3^2*a1-b2*b3*a2*a1*b1+a3^2*b1^3 ...
-2*a3*a1*b1^2*b3+b3^2*a1^2*b1+b3^3+b1^2*a2^2*b3-2*b3^2*a2*b1);
q0 = (-d0*a3*b3^2-d0*b3^2*a1^3-d0*a3^2*b1*b2-d0*a3^2*b1^2*a1-d5*a1*b1*b2-d3*b3*a2*b1+d4*b3*a1*b1+d3*b1*a3*b2 ...
-d4*b3*b2+d2*b3*a2*b2+d2*b3*a3*b1-d2*a3*b2^2-d1*a3*b2*a2*b1-d2*b3^2*a1+d1*b2^2*a1*a3+d1*a3^2*b1^2+d1*a3*b2*b3 ...
-2*d1*a3*a1*b1*b3-d1*b3*b2*a2*a1+d1*b3*a2^2*b1+d0*b2*a1*a2*b1*a3-d0*b3*a1*b1*a2^2+d1*b3^2*a1^2+d0*b2^2*a3*a2 ...
-d0*b2^2*a1^2*a3-d1*b3^2*a2+2*d0*a3*b3*a1^2*b1-d4*b1^2*a3+d0*b3*b2*a2*a1^2-d5*b1*b3-d0*a3*a1*b3*b2 ...
+2*d0*b3^2*a2*a1-d0*b3*b2*a2^2+d5*b1^2*a2+d3*b3^2+d5*b2^2)/ ...
(-a3*b2^3+b2^2*a3*a1*b1+b2^2*b3*a2-b1^2*a3*a2*b2+3*b1*a3*b2*b3-b2*b3^2*a1-b2*b3*a2*a1*b1+a3^2*b1^3 ...
-2*a3*a1*b1^2*b3+b3^2*a1^2*b1+b3^3+b1^2*a2^2*b3-2*b3^2*a2*b1);
q1 = (d4*b3^2+d0*a3*b3^2*a1+d0*b3^2*a2^2-d1*a3*b3^2+d0*a3^2*b2^2-d5*b1^2*a3+d5*a1*b1^2*a2-d5*a1^2*b1*b2 ...
+d4*b3*a1^2*b1-d4*b3*a1*b2-d4*b3*a2*b1-d4*a3*a1*b1^2+d4*b1*a3*b2+d3*b3*a2*b2+d3*b3*a3*b1+d5*a1*b2^2 ...
-d3*b3*a2*a1*b1+d3*b2*a3*a1*b1-d2*a3*b2*a2*b1+d2*b3*a2^2*b1-d2*a3*a1*b1*b3+d2*a3*b2*b3-d1*a3^2*b1*b2 ...
+d1*b2^2*a3*a2-d5*b3*b2-d1*b3*b2*a2^2-d2*b3^2*a2+d1*b3^2*a2*a1-d0*a3^2*b1^2*a2+2*d0*a3*b3*a2*a1*b1 ...
+d0*b2*a3*a2^2*b1-d0*b3*a2^3*b1-d0*b2^2*a2*a1*a3-d0*a3^2*b1*b3-d3*a3*b2^2+d0*b3*b2*a2^2*a1-2*d0*b3*a3*a2*b2 ...
+d2*a3^2*b1^2-d0*b3^2*a2*a1^2)/ ...
(-a3*b2^3+b2^2*a3*a1*b1+b2^2*b3*a2-b1^2*a3*a2*b2+3*b1*a3*b2*b3-b2*b3^2*a1-b2*b3*a2*a1*b1+a3^2*b1^3 ...
-2*a3*a1*b1^2*b3+b3^2*a1^2*b1+b3^3+b1^2*a2^2*b3-2*b3^2*a2*b1);
q2 = (d5*b1*a3*b2-d5*b2*a2*a1*b1+d4*a3*a1*b1*b2-d3*a3*b3*a1*b1+d2*a3*b3*a2*b1-d1*a3*b3*a2*b2+d0*a3^2*b2*a2*b1 ...
-d0*a3*b3*a2^2*b1+2*d0*a3^2*a1*b1*b3+d0*a3*b3*b2*a2*a1+d5*b3^2+d3*a3^2*b1^2-d2*a3*b3^2+d1*a3^2*b2^2 ...
-d0*a3^3*b1^2+d5*b1^2*a2^2+d5*a2*b2^2-d4*a3*b2^2-d2*a3^2*b1*b2-d1*a3^2*b3*b1+d1*a3*b3^2*a1-d0*a3^2*b2^2*a1 ...
-d0*a3^2*b2*b3-d0*a3*b3^2*a1^2+d0*a3*b3^2*a2-2*d5*b3*a2*b1+d5*b3*a1^2*b1-d5*a3*a1*b1^2-d5*b3*a1*b2 ...
-d4*a3*b1^2*a2+d4*a3*b1*b3+d3*a3*b3*b2)/ ...
(-a3*b2^3+b2^2*a3*a1*b1+b2^2*b3*a2-b1^2*a3*a2*b2+3*b1*a3*b2*b3-b2*b3^2*a1-b2*b3*a2*a1*b1+a3^2*b1^3 ...
-2*a3*a1*b1^2*b3+b3^2*a1^2*b1+b3^3+b1^2*a2^2*b3-2*b3^2*a2*b1);
% 2nd condition:
switch (rs_type)
case 1, %step:
% B = b1*z^-1 + b2*z^-2 + b2*z^-3 F = 1 - z^-1
% R = r0 S = s0 + s1*z^-1 + s2*z^-2 + s3*z^-3 + s4*z^-4
% [ 0 1 0 0 0 0] [r0] [d0]
% [b1 -1 1 0 0 0] [s0] [d1]
% [b2 0 -1 1 0 0] * [s1] = [d2]
% [b3 0 0 -1 1 0] [s2] [d3]
% [ 0 0 0 0 -1 1] * [s3] = [d4]
% [ 0 0 0 0 0 -1] [s4] [d5]
r0 = (d0+d1+d2+d3+d4+d5)/(b1+b3+b2);
r1 = 0;
case 2, %ramp
% B = b1*z^-1 + b2*z^-2 + b3*z^-3 F = 1 - 2*z^-1 + z^-2');
% R = r0 + r1*z^-1 S = s0 + s1*z^-1 + s2*z^-2 + s3*z^-3');
% [ 0 0 1 0 0 0] [r0] [d0]
% [b1 0 -2 1 0 0] [r1] [d1]
% [b2 b1 1 -2 1 0] * [s0] = [d2]
% [b3 b2 0 1 -2 1] [s1] [d3]
% [ 0 b3 0 0 1 -2] [s2] [d4]
% [ 0 0 0 0 0 1] [s3] [d5]
r0 = (4*d0*b3+3*d0*b2+2*d0*b1+3*d1*b3+d1*b1+2*d1*b2+2*d2*b3+d2*b2-d3*b1+b3*d3-2*d4*b1-d4*b2+d5*b3 ...
-2*d5*b2-5*d5*b1)/(b1+b2+b3)^2;
r1 = (-3*d0*b3-d0*b1-2*d0*b2-2*d1*b3-d1*b2+d2*b1-d2*b3+2*d3*b1+d3*b2+d4*b3+2*d4*b2+3*d4*b1+2*d5*b3 ...
+5*d5*b2+8*d5*b1)/(b1+b2+b3)^2;
case 3, %sin(om*t/T0)
om = 2*pi*rs_freq*T0;
% B = b1*z^-1 + b2*z^-2 + b3*z^-3 F = 1 - 2*cos(om)*z^-1 + z^-2');
% R = r0 + r1*z^-1 S = s0 + s1*z^-1 + s2*z^-2 + s3*z^-3');
% [ 0 0 1 0 0 0] [r0] [d0]
% [b1 0 -2*cos(om) 1 0 0] [r1] [d1]
% [b2 b1 1 -2*cos(om) 1 0] * [s0] = [d2]
% [b3 b2 0 1 -2*cos(om) 1] [s1] [d3]
% [ 0 b3 0 0 1 -2*cos(om)] [s2] [d4]
% [ 0 0 0 0 0 1] [s3] [d5]
r0 = (2*d0*b1*cos(om)+4*d0*b2*cos(om)^2-d0*b2+8*d0*b3*cos(om)^3-4*d0*b3*cos(om)+d1*b1+2*d1*b2*cos(om) ...
+4*d1*b3*cos(om)^2-b3*d1+d2*b2+2*d2*b3*cos(om)-d3*b1+b3*d3-2*d4*b1*cos(om)-d4*b2-4*d5*b1*cos(om)^2 ...
-d5*b1-2*d5*b2*cos(om)+d5*b3)/(b1^2+2*b1*b2*cos(om)+4*b1*b3*cos(om)^2-2*b1*b3+b2^2+2*b2*b3*cos(om)+b3^2);
r1 = -(d0*b1+2*d0*b2*cos(om)+4*d0*b3*cos(om)^2-d0*b3+d1*b2+2*d1*b3*cos(om)-d2*b1+d2*b3-2*d3*b1*cos(om)-d3*b2 ...
-4*d4*b1*cos(om)^2+d4*b1-2*d4*b2*cos(om)-d4*b3-8*d5*b1*cos(om)^3-4*d5*b2*cos(om)^2-d5*b2-2*d5*b3*cos(om))/ ...
(b1^2+2*b1*b2*cos(om)+4*b1*b3*cos(om)^2-2*b1*b3+b2^2+2*b2*b3*cos(om)+b3^2);
end;
param=[r0; r1; q0; q1; q2; p0; p1; p2];
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