Research Article
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. |
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