Hi.

I'm working on modeling a system which have resulted in a system of first order nonlinear differential equations s'(t) = f(t, s(t), u(t))
with state vector s(t) and control input u(t) and s(t), u(t) \in R^3
The measurements are simply given by y(t) = s(t).

The continuous time model is embedded in a digital control loop where there output y(n) is a sampled version of y(t) with zero order hold and Ts = 0.1 s. Similarly the discrete control inputs u(n) is converted through zero order hold to u(t) with the same sample time.

I now want to write this model as: s(n + 1) = g(n, s(n), u(n)). I know how to do this is for a linear continous time continous model s'(t) = Ax(t) + Bu(t) with the c2d fuction but I am in doubt how to do this for the nonlinear model.

Should I linearize the continous time differential equation first or what is the best method?

Thanks in advance.

I'm working on modeling a system which have resulted in a system of first order nonlinear differential equations s'(t) = f(t, s(t), u(t))

The continuous time model is embedded in a digital control loop where there output y(n) is a sampled version of y(t) with zero order hold and Ts = 0.1 s. Similarly the discrete control inputs u(n) is converted through zero order hold to u(t) with the same sample time.

I now want to write this model as: s(n + 1) = g(n, s(n), u(n)). I know how to do this is for a linear continous time continous model s'(t) = Ax(t) + Bu(t) with the c2d fuction but I am in doubt how to do this for the nonlinear model.

Should I linearize the continous time differential equation first or what is the best method?

Thanks in advance.