Method and apparatus for substantially improving the throughput of circuit simulators

Claim 1

A method for simulating with a circuit simulation processor a steady state operation of a periodic piece-wise linear switched system having a plurality of switched states; comprising the steps of: defining a cycle of operation of the switched system; defining subintervals of the cycle in which different switched states in the switching system define a different system topology in the different subintervals; determining an initial value of a state vector for the periodic piece-wise linear switched system at the beginning of the cycle; simulating a single cycle of operation to obtain a final value of the state vector for the periodic piece-wise linear switched system at the end of the cycle; comparing the initial and final values of the state vector to determine if a steady state condition in the simulation of operation has been achieved; wherein the improvement comprises: computing a subinterval Jacobian matrix for each subinterval by computing a subinterval state transition matrix; and adding a correction square matrix to the subinterval state transition matrix to account for changes in subinterval time durations; computing a cycle Jacobian matrix by subtracting an identity matrix from a product of all computed subinterval Jacobian matrices; adjusting the value of the initial value of the state vector to a new value form the computed cycle Jacobian matrix through a truncated power-series procedure; and repeating the above described steps subsequent to the step of determining an initial value until steady state simulation is achieved.

Claim 2

A method for simulating with a circuit simulation processor a steady state operation of a periodic piece-wise linear switched system having a plurality of switched states; comprising the steps of: defining a cycle of operation of the switched system; defining subintervals of the cycle in which different switched states in the switching system define a different system topology in the different subintervals; determining an initial value of a state vector for the periodic piece-wise linear switched system at the beginning of the cycle; simulating a single cycle of operation to obtain a final value of the state vector for the periodic piece-wise linear switched system at the end of the cycle; comparing the initial and final values of the state vector to determine if a steady state condition in the simulation of operation has been achieved; wherein the improvement comprises: computing a subinterval Jacobian matrix for each subinterval by computing a subinterval state transition matrix; and adding a correction square matrix to the subinterval state transition matrix to account for changes in subinterval time durations; computing a cycle Jacobian matrix by subtracting an identity matrix from a product of all computed subinterval Jacobian matrices; adjusting the value of the initial value of the state vector to a new value form the computed cycle Jacobian matrix through a truncated power-series procedure; and repeating the above described steps subsequent to the step of determining an initial value until steady state simulation is achieved.

Claim 4

An apparatus for modeling an operation of a periodic piece-wise linear system to a predetermined accuracy; comprising: first input means for accepting and setting up a specific topology for each switched subinterval occurring in each cycle of operation of the periodic piece-wise linear system; second input means for accepting an initial value of a state vector for the periodic piece-wise linear system at the beginning of a cycle of operation of the periodic piece-wise linear system; means for simulating a single cycle of operation of the periodic piece-wise linear system to obtain a final value of the state vector for the wise linear system to obtain a final value of the state vector for the periodic piece-wise linear system at the end of the cycle; means for comparing the initial and final values of the state vector to determine if a steady state operating condition has been achieved; wherein the improvement comprises; means for dividing each cycle into a plurality of subintervals for each switched subinterval of the periodic piece-wise linear system and computing a subinterval Jacobian matrix for each subinterval by computing a subinterval state transition matrix; and adding a correction square matrix to the subinterval state transition matrix to account for changes in subinterval time durations; means for computing a cycle Jacobian matrix by subtracting an identity matrix from a product of all computed subinterval Jacobian matrices; means for adjusting the value of the initial value of the state vector to a new value from the computed cycle Jacobian matrix through a truncated power-series procedure; means for repeating the above described opertions until the predetermined accuracy of steady state operation is achieved.

Claim 5

An apparatus for modeling an operation of a periodic piece-wise linear system to a predetermined accuracy; comprising: first input means for accepting and setting up a specific topology for each switched subinterval occurring in each cycle of operation of the periodic piece-wise linear system; second input means for accepting an initial value of a state vector for the periodic piece-wise linear system at the beginning of a cycle of operation of the periodic piece-wise linear system; means for simulating a single cycle of operation of the periodic piece-wise linear system to obtain a final value of the state vector for the wise linear system to obtain a final value of the state vector for the periodic piece-wise linear system at the end of the cycle; means for comparing the initial and final values of the state vector to determine if a steady state operating condition has been achieved; wherein the improvement comprises; means for dividing each cycle into a plurality of subintervals for each switched subinterval of the periodic piece-wise linear system and computing a subinterval Jacobian matrix for each subinterval by computing a subinterval state transition matrix; and adding a correction square matrix to the subinterval state transition matrix to account for changes in subinterval time durations; means for computing a cycle Jacobian matrix by subtracting an identity matrix from a product of all computed subinterval Jacobian matrices; means for adjusting the value of the initial value of the state vector to a new value from the computed cycle Jacobian matrix through a truncated power-series procedure; means for repeating the above described opertions until the predetermined accuracy of steady state operation is achieved.

Claim 8

A method for simulating steady state operation of a periodic piece-wise switched linear system and where the switched linear system is modeled by k different switching topologies and the system being piece-wise linear in each individual topology, the method comprising the steps of: defining a cycle of operation of the switched system; defining k subintervals of the cycle in which different switched states in the switched linear system define a different system topology in the different subintervals; describing the system by a linear vector differential equation dx/dt=A.sub.k x+B.sub.k u and a linear vector algebraic equation Y=C.sub.k x+D.sub.k u for each of the k different topologies; selecting an initial state vector x i of the system for the beginning of a cycle of opertion of the system; simulating a single cycle of operation to calculate a final state vector x f of the system for the ending of a cycle of operation of the system; defining a change in the state vector over one switching cycle by defining the vector function F(x.sub.i)=x.sub.f -x.sub.i in terms of the initial state vector x i and the final state vector x f; wherein the improvement comprises: continuing with the following steps if x f does not equal x i: calculating an individual subinterval sensitivity matrix J k for each piece-wise linear subinterval of the cycle by computing a state transition matrix ωk(tk) and a correction square matrix r k and J.sub.k =ω.sub.k (t.sub.k)+r.sub.k to account for variations in subinterval time durations; computing a steady-state Jacobian matrix J(x i ) by the operation J(x.sub.i)=J.sub.k J.sub.k -1 . . . J.sub.2 J.sub.1 -I; correcting the value of the initial state vector x i by the j operation x.sub. <x.sub.i -[J(x.sub.i ].sup.-1 F(x.sub.i); repeating the above step of simulating s single cycle of operation to calculate a final state vector x f of the system and continuing subsequent steps until x f substantially equal x i .

Claim 9

A method for simulating steady state operation of a periodic piece-wise switched linear system and where the switched linear system is modeled by k different switching topologies and the system being piece-wise linear in each individual topology, the method comprising the steps of: defining a cycle of operation of the switched system; defining k subintervals of the cycle in which different switched states in the switched linear system define a different system topology in the different subintervals; describing the system by a linear vector differential equation dx/dt=A.sub.k x+B.sub.k u and a linear vector algebraic equation Y=C.sub.k x+D.sub.k u for each of the k different topologies; selecting an initial state vector x i of the system for the beginning of a cycle of opertion of the system; simulating a single cycle of operation to calculate a final state vector x f of the system for the ending of a cycle of operation of the system; defining a change in the state vector over one switching cycle by defining the vector function F(x.sub.i)=x.sub.f -x.sub.i in terms of the initial state vector x i and the final state vector x f; wherein the improvement comprises: continuing with the following steps if x f does not equal x i: calculating an individual subinterval sensitivity matrix J k for each piece-wise linear subinterval of the cycle by computing a state transition matrix ωk(tk) and a correction square matrix r k and J.sub.k =ω.sub.k (t.sub.k)+r.sub.k to account for variations in subinterval time durations; computing a steady-state Jacobian matrix J(x i ) by the operation J(x.sub.i)=J.sub.k J.sub.k -1 . . . J.sub.2 J.sub.1 -I; correcting the value of the initial state vector x i by the j operation x.sub. <x.sub.i -[J(x.sub.i ].sup.-1 F(x.sub.i); repeating the above step of simulating s single cycle of operation to calculate a final state vector x f of the system and continuing subsequent steps until x f substantially equal x i .