US2019107072A1PendingUtilityA1
Hybrid partial and full step quadratic solver for model predictive control of diesel engine air path flow and methods of use
Assignee: TOYOTA ENG & MFG NORTH AMERICAPriority: Jun 17, 2016Filed: Dec 10, 2018Published: Apr 11, 2019
Est. expiryJun 17, 2036(~9.9 yrs left)· nominal 20-yr term from priority
F02B 37/22F02M 26/05Y02T10/47F02D 41/1401Y02T10/42F02D 41/005F02D 41/0002F02D 2041/1433F02D 41/0077F02D 41/28F02D 41/0007F02D 41/0005F02D 41/1406F02D 2041/1412Y02T10/40F02D 41/0065Y02T10/12F02D 2200/0406F02D 2041/0022F02D 41/0072F02D 2041/0017F02D 2041/1436F02D 2041/286
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Claims
Abstract
Methods and systems for use of model predictive control (MPC) controllers utilizing hybrid, quadratic solvers to solve a linear feasibility problem corresponding to a nonlinear problem for an internal combustion engine plant such as a diesel engine air path. The MPC solves a convex, quadratic cost function having optimization variables and constraints and directs the plant per the output solutions to optimize plant operation while adhering to regulations and constraints. The problem includes a combination of iterative and direct calculations in the primal space depending on whether a partial step (iterative) or a full step (direct) is attempted. Further, primal and dual space array matrices are pre-computed and stored offline and are retrieved via use of a unique identifier associated with a specific active set for a set of constraints. Such hybrid and/or offline calculations allow for a reduction in computational power while still maintaining accuracy of solution results.
Claims
exact text as granted — not AI-modifiedWhat is claimed is:
1 . A method for controlling an internal combustion engine having a variable geometry turbine (VGT), an exhaust gas recirculation (EGR) valve, and an EGR throttle, the method comprising:
solving a linear quadratic problem with a predictive model comprising an updating algorithm in order to determine: (i) a requested optimized VGT lift that meets one or more constraints; and (ii) a requested optimized EGR valve flow rate that meets the one or more constraints, wherein solving the linear quadratic problem includes:
determining whether to take a determined step comprising one of a primal partial step and a primal full step at each iteration, and
taking the determined step at each iteration until the linear quadratic problem is solved by the updating algorithm, wherein:
taking the primal partial step comprises performing an iterative calculation, and
taking the primal full step comprises performing a direct calculation;
generating the requested optimized VGT lift responsive to an engine intake manifold pressure by controlling the VGT; and generating the requested optimized EGR valve flow rate responsive to an EGR rate by controlling the EGR valve and the EGR throttle.
2 . The method of claim 1 , further comprising:
setting one or more engine operating parameters as the one or more constraints to form a non-linear problem; and deriving the linear quadratic problem based on the non-linear problem, wherein the linear quadratic problem is convex and time-varying.
3 . The method of claim 2 , wherein the linear quadratic problem to solve comprises the following equation:
min
J
(
)
=
1
2
T
+
ℋ
T
s
.
t
.
≤
where is a time varying linear term in the cost function; is a constant quadratic term in the cost function; is a constant constraint matrix; is a time varying constraint vector; and is one or more optimization variables comprising time varying control inputs.
4 . The method of claim 3 , wherein the time varying control inputs comprise at least one of the a VGT lift and an EGR flow, and further comprising adding Lagrangian multipliers μ to determine a solution for optimization variable(s) * and Lagrangian multiplier(s) μ* that are greater than or equal to zero to satisfy dual feasibility, while utilizing only active, feasible constraints of the one or more constraints.
5 . The method of claim 4 , wherein:
the VGT comprises turbine input vanes configured to be angled to be opened, partially opened, or closed; and the active, feasible constraints comprises at least one of a maximum EGR rate, a minimum EGR rate, a maximum EGR flow command, a minimum EGR flow command, a maximum VGT lift closed command to control a maximum amount of closure of the turbine input vanes, and a minimum VGT lift closed command to control a minimum amount of closure of the turbine input vanes.
6 . The method of claim 5 , further comprising simplifying the determined solution for a current active set list L and to define iterative and direct calculation approaches to determine how to move from the current active set list L to a new active set list L+1, resulting in the following simplified HQPKWIK equation:
L
+
1
=
{
L
+
zv
knext
t
Primal
Partial
(
Half
)
Step
-
T
L
+
1
U
(
T
L
+
1
U
)
T
ℋ
+
T
L
+
1
C
R
L
+
1
-
T
L
+
1
Primal
Full
Step
μ
L
+
1
=
μ
L
-
rv
knext
t
Dual
Step
where t is a minimum length that still maintain dual feasibility, v knext is a next constraint to be added to a current constraint set list, z is an array that is indicative of a search direction in primal space, and r is an array that is indicative of a search direction in dual space, such that:
z=T L U ( T L U ) T
r=R L 7 −1 ( T L C ) T .
7 . The method of claim 6 , further comprising computing the z and r arrays on-line.
8 . The method of claim 6 , further comprising pre-computing portions of the z and r arrays off-line.
9 . The method of claim 8 , further comprising retrieving the z and r arrays after a determination of a unique identifier at least partially based on the current active set list.
10 . The method of claim 9 , wherein the determination of the unique identifier utilizes a conversion of one or more binary numbers of the current active set list to a decimal value, and the unique identifier comprises the decimal value.Join the waitlist — get patent alerts
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