Is there any in-built function/ method to customize state-space model in MATLAB

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Siddhanth Sunil Shah
回答： Kartik Saxena 2024-1-2
If the state space model is of the form:
dx/dt = Ax + Bu
y = Cx + Du
we can easily assign the values of A, B, C, D in matlab and get a transfer function using the ss and tf commands.
However if the state space model is of the form say:
dx/dt = Ax + Bu*e^t
y = Cx + Du*e^t
y(t) = 0 for all t>=0
and Cx + Du*e^t = 0 for all t>=0
Do we have any in-built function in MATLAB through we can customize our state-space model and the provide the values of A, B, C, D to get our transfer function G?
  2 个评论
Paul
Paul 2022-1-9
What do you mean by
u*e^t
Is that convolution or multiplication?
Also, the constraint y(t) = 0 is confusing. I mean, if y(t) = 0, then the transfer function is zero (assuming an LTI system).
Siddhanth Sunil Shah
Siddhanth Sunil Shah 2022-1-9
编辑：Siddhanth Sunil Shah 2022-1-9
u*e^t is actually a multiplication. Its Bue^t.
Yes that is what I thought too that the transfer function should be zero but apparently it should'nt be and should be possible using the eigen value formulation of the state space representation.

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回答（1 个）

Kartik Saxena
Kartik Saxena 2024-1-2
Hi,
In MATLAB, the standard state-space to transfer function conversion using `ss` and `tf` commands assumes a linear time-invariant (LTI) system. The system you've described includes a time-varying element `e^t` in the input matrix and direct transmission matrix, which makes it a time-varying system. MATLAB's Control System Toolbox does not directly support conversion of time-varying state-space models to transfer functions using built-in commands.
However, you can represent time-varying systems using functions or handle classes to create custom behavior. Here's a general approach to simulate such systems:
1. Define the System Matrices as Functions: You can define `A`, `B`, `C`, and `D` as functions of time if they vary with time. In your case, `B(t) = B*e^t` and `D(t) = D*e^t`.
2. Simulate the System: Use MATLAB's numerical solvers (like `ode45`) to simulate the system's response to an input. You'll need to define the differential equations in a function that the solver can use.
I hope this resolves your issue.

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