A Two-Step Global Maximum Error Controller-Based TPWL MOR with POD Basis Vectors and Its Applications to MEMS

Algorithm 2

Improved TPWL-GMEC method.

(preliminary LP selection)

(1) Given a training input and a threshold ;

(2) Choose the initial state as the first LP candidate , and set ;

(3) Simulate the nonlinear system (1) to obtain the state-set and select LP

candidates:

for  

Simulate the nonlinear system (1) to get the state and record it;

if  ,  then select as the th LP candidate , record

the corresponding time instant , and set ;

end for

(secondary LP selection)

(4) Given the maximum error limit ;

(5) Select a set of states from the state-set of the nonlinear system;

(6) Construct the POD projection matrix through applying the SVD algorithm

to the set of states, that is, ;

(7) Choose the first LP candidate as the first LP , and set ;

(8) Built the current TPWL model;

(9) Simulate the current TPWL model to get the responses ;

(10) Find out the maximum error state :

Set and

for  

Compute ;

if    then  , ;

end for

(11) if   and has not been selected as a LP, then  select the

LP , set , and go to ();

(12) if    then return the selected LPs and end the loop.