Modeling and Control of Multi Stage Rolling Mill Process

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04 Aug 2010 (Updated )

This demo shows plant modeling and controller design for a multi stage rolling mill process.

multi_stand_init.m
clear all;
%Rolling mill parameters
g         = 9.81;     %Gravity (m/s/s)
Wplate    = 1;        % Plate width (m)
rho       = 7800;     %Density of steel in Kg/m^3
E         = 200e9;    %Youngs modulus of steel (N/m^2) 200e9 for steel 
% Lplate=0.01;



%% Motor parameters driving looper
% % Kdamping_looper  = 0.12;      %Motor damping (Nm/rad/s)
% % KTorque_looper   = 4;       %Motor torque constant (Nm/A)
% % Kemf_looper      = 0.21;      %Motor back emf constant (V/rad/s)
% % Rarmature_looper = 1.9;       %Motor armature resistance (ohm)
% % Larmature_looper = 0.54e-3;   %Motor armature inductance (H)
% % DC0_looper       = 2*pi*Vroll/60*(Kdamping*Rarmature/KTorque+Kemf);  %Nominal armature voltage (V)
% % Ia0_looper       = 2*pi*Vroll/60*Kdamping/KTorque;                   %Nominal armature current (A)

%% Initial controller parameters
% % Kthickness = 1;     %Proprotional gain for thickness loop
% % Kvelocity  = 1;     %Proportional gain for velocity loop
% % Klooper    = 1000;
Lstep = 0.005;      %Plate thickness step change
% % Vstep = 0.1;        %Percentage change in plate speed reference

%% Noise source parameters
% % Fmax   = 4e4;    %approximate maximum force
% % Snoise = 1;      %Band limited noise sample time
% % Pnoise = 0.0;  %Band limited noise covariance

%% Hydraulic settings
% % % HydPressure = 50e6;   %Pressure source (Pa)
% % % Lpiston     = 0.01;   %Piston length (m)
% % % ValveIC   = 0.05*Lpiston;    %Initial valve opening, prevent initial condition at hardstop

%Values for metal properties, from
%http://www.engineeringtoolbox.com/young-modulus-d_773.html
Temperature = [-325 -200 -100 70 200 300 400 500 600 700 800 900 1000 1100 1200];
Temperature = 5/9*(Temperature-32); %Convert F->C
Metals = {...
   'Gray cast iron'; ...
   'Carbon steel C <= 0.3%'; ...
   'Carbon steel C => 0.3%'; ...
   'Carbon-moly steels'; ... 
   'Nickel steels Ni 2% - 9%'; ...    
   'Cr-Mo steels Cr 1/2% - 2%'; ... 
   'Cr-Mo steels Cr 2 1/4% - 3%'; ... 
   'Cr-Mo steels Cr 5% - 9%'; ... 
   'Chromium steels Cr 12%, 17%, 27%'};
YoungsMod = [...
   13.4 13.2 12.9 12.6 12.2 11.7 11.0 10.2 nan  nan  nan  nan  nan  nan  nan; ...
   31.4 30.8 30.2 29.5 28.8 28.3 27.7 27.3 26.7 25.5 24.2 22.4 20.4 18.0 nan; ...
   31.2 30.6 60.0 29.3 28.6 28.1 27.5 27.1 26.5 25.3 24.0 22.2 20.2 17.9 15.4; ...
   31.1 30.5 29.9 29.2 28.5 28.0 27.4 27.0 26.4 25.3 23.9 22.2 20.1 17.8 15.3; ... 
   29.6 29.1 28.5 27.8 27.1 26.7 26.1 25.7 25.2 24.6 23.0 nan  nan  nan  nan; ...    
   31.6 31.0 30.4 29.7 29.0 28.5 27.9 27.5 26.9 26.3 25.5 24.8 23.9 23.0 21.8; ... 
   32.6 32.0 31.4 30.6 29.8 29.4 28.8 28.3 27.7 27.1 26.3 25.6 24.6 23.7 22.5; ... 
   32.9 32.3 31.7 30.9 30.1 29.7 29.0 28.6 28.0 27.3 26.1 24.7 22.7 20.4 18.2; ... 
   31.2 30.7 30.1 29.2 28.5 27.9 27.3 26.7 26.1 25.6 24.7 23.2 21.5 19.1 16.6];
YoungsMod = 6894.8*1e6*YoungsMod;    %Convert Mpsi -> Pa
KfromT = pi*(0.001)^2*YoungsMod/0.1; %Approximate spring stiffness

disp('Mill parameters set')

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