Page 578 - Mechatronics with Experiments

JWST499-Cetinkunt
JWST499-c07
564 MECHATRONICS Printer: Yet to Come October 9, 2014 8:41 254mm×178mm
x_v = z(3) ;
xdot_v = z(4) ;
p_a = z(5) ;
p_b = z(6) ;
y = z(7) ;
ydot = z(8) ;

zdot=zeros(8,1) ;

% ODEs....
% Pump flow rate and pressure, and relief-valve model (instantaneously
% acting)
Q_p = D_p ∗ w_shaft ;

if p_p < p_max
zdot(1)= (beta/V_hose_pv)∗(Q_p - Q_v) ;
Q_r = 0.0 ;
else
zdot(1) = 0.0 ;
Q_r = Q_p - Q_v ;
end

% Amplifier and servo valve electrical dynamics

zdot(2) = K_a ∗ (1/tau_a)∗ (- z(2) + i_cmd) ;
T_v = K_t ∗ z(2) ;

% Servo valve stage two spool position and torque relationship

if ((x_v/x_vmax) <= 0.4)
w_n = 2∗pi∗75 ; % rad/sec
else
w_n = 2∗pi∗ (75 - ( ((x_v/x_vmax) - 0.4) ∗ ((75-25)/(1.0-0.4)) ));
% rad/sec
end
zdot(3) = z(4) ;
zdot(4) = (- 2 ∗ c_v ∗ w_n ∗ z(4) - w_nˆ2 ∗ z(3)) + (x_vmax/T_vmax)
∗ w_nˆ2 ∗ T_v ;

if x_v >= 0.0
Q_pa = Q_rv ∗ abs(x_v/x_vmax) ∗ ((p_p - p_a)/p_r)ˆ0.5 ;
Q_bt = Q_rv ∗ abs(x_v/x_vmax) ∗ ((p_b - p_t)/p_r)ˆ0.5 ;
Q_v = Q_pa ;
zdot(5) = (beta/(V_hose_va + y ∗ A_a))∗(Q_pa - ydot ∗ A_a) ;
zdot(6) = (beta/(V_hose_vb + (l_cyl - y) ∗ A_b))∗(-Q_bt + ydot ∗ A_b);
else
Q_at = Q_rv ∗ abs(x_v/x_vmax) ∗ ((p_a - p_t)/p_r)ˆ0.5 ;
Q_pb = Q_rv ∗ abs(x_v/x_vmax) ∗ ((p_p - p_b)/p_r)ˆ0.5 ;
Q_v = Q_pb ;
zdot(5) = (beta/(V_hose_va + y ∗ A_a))∗(-Q_at - ydot ∗ A_a) ;
zdot(6) = (beta/(V_hose_vb + (l_cyl - y) ∗ A_b))∗(Q_pb + ydot ∗ A_b);
end