Speeding up Simulation with Higher Order Transfer Function

For a Higher Order Transfer Function the simulation is very slow due to small step sizes taken by the solver. How can we speed up the simulation in Simulink R2021a?

Answer 1

[MathWorks Support Team]

The simulation runs in the order of e-8 seconds for a model containing a transfer function of 7th order in Simulink R2021a. If the simulation step-size is increased manually the simulation fails due to singularity in the transfer function. 

In the case of Higher Order Transfer Functions, the solver will choose a small step-size to properly capture the high-frequency dynamics resulting from Higher Order Transfer Function. By setting the step-size manually it is prone to error because of the large variation between two successive steps.

These are the possible workarounds if simulation speed needs to be increased-

• Using Accelerator or Rapid-Accelerator Mode of Simulation if the accuracy is not to be reduced.
• If there are more simulations, they could be simulated parallelly using "parsim" function.
• If a reduction in accuracy of the simulation is acceptable "modred" function can be used to convert the transfer function to state-space model by removing negligible states.

The following code snippet provides an example of converting the transfer function to state-space model.

num = [ 3 0 ];
den = [ 2e-34 14e-25 1e-16 2e-09 0.0023 39.1 2.05e07];
sys = tf(num,den) % transfer function of 7th order
[sys,g] = balreal(sys)  % Compute balanced realization
elim = (g<1e-8)         % Small entries of g are negligible states
%rsys is a state space object
rsys = modred(sys,elim) % Remove negligible states

For more information on the functions used in the above code snippet please refer to the following documentation links

1. "modred" - https://www.mathworks.com/help/releases/R2021a/control/ref/ss.modred.html
2. "tf" - https://www.mathworks.com/help/releases/R2021a/control/ref/tf.html
3. "parsim" -https://www.mathworks.com/help/releases/R2021a/simulink/slref/parsim.html