Hi,

I have a transfer function for a 2x2 MIMO problem, of the form G=[G11 G12; G21 G22], consisting of first-order lags with time delay. I also
have two PI controllers that are supposed to control this system. I
would like to plot the performance of these controllers, but I only
know how to work with ODEs in the time domain.

I know how to convert a SISO transfer function into an ODE, but after much frustration I'm stuck on the MIMO case. I am aware of this equation:

Y1(s) = G11(s)R1(s) + G12(s)R2(s) Y2(s) = G21(s)R1(s) + G22(s)R2(s)

How do I convert that into:

dy1/dt = f(u1,u2) dy2/dt = f(u1,u2)

where u1 and u2 are the outputs of the PI controllers?

Or is there some other way of plotting y1 and y2 as a function of time?

Many heart-felt thanks.

I have a transfer function for a 2x2 MIMO problem, of the form G=[G11 G12; G21 G22], consisting of first-order lags with time delay. I also

I know how to convert a SISO transfer function into an ODE, but after much frustration I'm stuck on the MIMO case. I am aware of this equation:

Y1(s) = G11(s)R1(s) + G12(s)R2(s) Y2(s) = G21(s)R1(s) + G22(s)R2(s)

How do I convert that into:

dy1/dt = f(u1,u2) dy2/dt = f(u1,u2)

where u1 and u2 are the outputs of the PI controllers?

Or is there some other way of plotting y1 and y2 as a function of time?

Many heart-felt thanks.