Hybrid Quadratic Solver for Diesel Engine MPC
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Solution Overview
Problem
Existing quadratic solvers for internal combustion engines, particularly in diesel engines with variable geometry turbines and exhaust gas recirculation systems, face challenges in achieving reduced computational time and increased accuracy while meeting stringent emission regulations.
Innovation Solution
The implementation of hybrid quadratic solvers, such as partial and full step methods, within a model predictive control framework that uses predictive models and updates algorithms to determine optimized VGT lift and EGR valve flow rates, allowing for iterative and direct calculations based on primal and dual space arrays to satisfy constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional quadratic solvers are used for model predictive control, then accuracy is maintained, but computational time increases
Solution Approach 1:
The quadratic solver is segmented into two distinct methods: a full step solver for high accuracy requirements and a partial step solver for reduced computational time. The system selectively applies each method based on operating conditions, thereby resolving the contradiction between accuracy and computational speed by dividing the problem into manageable segments with different solution strategies.
Solution Approach 2:
The system dynamically switches between full step and partial step quadratic solver methods based on real-time operating conditions and constraint activity. This dynamic adaptation allows the system to maintain accuracy when necessary while reducing computational time during normal operation, directly addressing the contradiction between precision and speed.
2Measurement precision
If full step quadratic solver is used, then accuracy is improved, but computational power required increases
Solution Approach 1:
The partial step quadratic solver implements partial action by solving only the necessary subset of constraints and variables at each iteration, rather than performing complete full-step calculations. This approach achieves sufficient accuracy for many operating conditions while significantly reducing computational power consumption, directly resolving the contradiction between precision and energy use.
Solution Approach 2:
The system changes the computational parameters by switching between different solver methodologies (full step vs. partial step) based on operating conditions. This parameter change allows the system to adjust the balance between accuracy and computational power consumption, using full step only when high precision is critical and partial step when lower power consumption is prioritized.
3Adaptability or versatility
If iterative calculations are performed for partial steps, then computational flexibility is improved, but convergence time increases
Solution Approach 1:
The solver employs periodic action by alternating between iterative partial step calculations and direct full step solutions. The system performs iterative calculations for partial steps when flexibility is needed, then periodically applies full step methods to ensure convergence and maintain accuracy, thereby balancing computational flexibility with convergence time through rhythmic application of different solution strategies.
Solution Approach 2:
When iterative calculations approach convergence or when operating conditions allow, the system skips remaining iterative steps and rushes through to a solution using direct calculation methods. This skipping strategy maintains computational flexibility where needed while reducing overall convergence time by not performing unnecessary iterative refinements, directly addressing the contradiction between adaptability and speed.
Data Source
AI summary
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.