%% Reduce steady-state parameter file (Reactor_sspar.r)
%% as siso_sspar ecxept that inputs/states have different meaning
%% Steady state for constant c_a, c_b and t=t_s and f=f_s
%% Unit volume Reactor:
v_r := 1;
%% Do the inputs first -- this avoids problems with reduce not
%% recognising that complicated expressions are zero
%% The exponentials.
e_1 := e^(-q_1/t_s);
e_2 := e^(-q_2/t_s);
e_3 := e^(-q_3/t_s);
%Steady-state input q needed to achieve steady-state t_s
q_s := -(
+ (t_0-t_s)*c_p*f_s
+ e_1*h_1*k_1*x1
+ e_2*h_2*k_2*x2
+ e_3*h_3*k_3*x1^2
);
%% The two inputs at steady-state
MTTu1 := f_s;
MTTu2 := q_s;
%States (masses)
x1 := c_a*v_r;
x2 := c_b*v_r;
%Thermal state
x3 := c_p*t_s*v_r;
%Load up the vectors
MTTx1 := x1;
MTTx2 := x2;
MTTx3 := x3;
MTTy1 := c_b;
MTTy2 := t_s;
%% Finally, solve for the steady-state concentrations
%% Solve for ca - a quadratic.
a := k_3*e_3; %ca^2
b := k_1*e_1 + f_s; %ca^1
c := -c_0*f_s;
c_a := (-b + sqrt(b^2 - 4*a*c))/(2*a);
%% solve for c_b
c_b := c_a*k_1*e_1/(f_s+k_2*e_2);
END;