Differntial equations and Initial conditions

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KaMATLAB 2021-3-28

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评论： KaMATLAB 2021-3-31

1. What are the main considerations for selecting initial conditions for solving dynamics equations using Matlab Simulink. For instance, setting the initial conditions in the continuous state block or integral block?

2. Is it possible to use a mathematcal expression or relation instead of a number as the initial condition in the integral block of Simulink?

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Paul 2021-3-28

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The initial conditions are set to represent the initial conditions of the system to be simulated. What other considerations might there be?
Yes. Any expression can be used that returns a value that is consistent with the requirements for the initial condition of the block in question.

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KaMATLAB 2021-3-28

Thank you for the reply. Now I have a system of differential equations that is about 32 set of differential equations. I have been able to use a single integrator for the simulink implementation. I have initial conditions that are mathematical expressions, which are derived from the steady state equillibrium conditions of each sets of the differential equations. My challenege is that I dont know how to insert each mathematical expressions of the initial conditions into the integral block. I have attached the intgeral block with some sample sets of initial condition which are constants.However I want expressions as attached also as the initial condition. The initial conditions are the calculated by equating the each differential equation to zero and make the desired state, the subject of the formula. Then it is the initial condition valeu at the equilibrium state. How do i realize such expression in the attached simulink matlab function i used to implement the system in the integral block.

May be there is a way to impelement Initial condition of large mathematical expression within the matlab function blokc used to solve the differential equations?

Thank you

Paul 2021-3-30

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Let X0 be the vector of initial conditions. One approach would be to compute

X0(1) = ....
X0(2) = ....

i.e., fill in each element X0 with the initial condition cacualtion in the base workspace. Then X0 is the Initial Condition parameter in the Integrator block.

KaMATLAB 2021-3-31