Transfer Function With Initial Conditions

Moreover the usual assumption in transfer functions is zero initial conditions.

Transfer function with initial conditions. I have defined defined a second order underdamped system in the time domain with a non zero initial condition for Y t but can not implement this in the laplace domain. The transfer function of a system is the Laplace transform of its impulse response under assumption of zero initial conditions. The transfer function of a linear system is the ratio of the Laplace Transform of the output to the Laplace Transform of the input ie Y sU s.

5152012 Initial conditions are preset to zero. Replacing s variable with linear operation in transfer function of a system the differential equation of the system can be obtained. To specify initial conditions convert to state-space form using tf2ss and use the State-Space block.

Control Control System Toolbox simulink system transfer function. 3112021 I am familiar with this process for polynomial functions. For example suppose we know two steady states for an input u and an output y.

To specify initial conditions convert to state-space form using tf2ss and use the State-Space block. However it is not clear how to do so when the impulse response is not a polynomial function. Function is known though the transfer function is more commonly used for the zero state response.

For more information type help tf2ss or. Consider a system whose time domain block diagram is. If the input to the system is a unit impulse then.

So first the problem has to be translated to a state-space representation with the desired states. Note that the equivalent transfer function G eq s which allows including nonzero initial conditions while utilizing the original input Us is a combination of the original transfer function Gs the nonzero initial conditions and the input. Initial Conditions for first derivative defined as a transfer function.