I have a Non-linear DE system shown on the picture, where the function f is closed form analytical function of theta. I am trying to find analytical solution for Laplace transform. My goal for Laplace transform is to find a direct relationship between the input (V) and the output theta. I tried the direct method and tried some math software but did not work. I also tried to linearize the system around some points but did not give good approximation within the operating range. The problem comes from Eq.1 as it is non-linear DE.
Does an analytical solution for Laplace of this system exist? If so, which method can be used?
I also want to mention that the function f can be an 8-terms Fourier series, or 4th order polynomial
I do not think so. The best way is to use some way of Laplace approximation. You may also try asymptotic ,Taylor series or Saddle point approximation.
Hi Ayham Aljawabrh
What exactly do you want to solve by finding direct relationship between the input Control Voltage (V) and the output Rotational Angle (θ) in the form of θ(V)?
Can you solve the following quadratic equation first?
A(θ)·(θ')² + B(θ)·θ' – K·i = 0
Dear Ayham Aljawabrh
I propose the following
Let dθ/dt =u
du/dt = d²θ)/dt² = F(u,θ)
In addition to the last equation
di/dt = G(i,u)
We obtain a nonlinear system of 3 equations.
Now we can study the system equilibrium points and stability.
I recommend the Hartman-Grobman theorem to linearize and study this new nonlinear dynamical system.
Best regards
Hi Yew-Chung Chak
I am trying to obtain a transfer function, let's call it g(s)=θ/V,
the goal is find a direct relationship between the input and the output. It will be used to study the effect of the input on the output, and try to linearize the system, based on this transfer function, why? we try to use the linear control methods and push it to control the nonlinear system.
What are A(θ), B(θ) are stand for? so, I can answer your question?
- Badges
- Science topic
- Similar topics
- Mathematics