Model Predictive Control Using Active Sets Solver for Embedded Optimization
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Solution Overview
Problem
Existing advanced control techniques, such as Model Predictive Control (MPC), face challenges in embedded applications due to limited computational resources and fast sampling periods, making real-time optimization difficult, especially for nonlinear systems which often require approximations to linear systems.
Innovation Solution
An MPC-based control strategy using an Active Sets solver for Quadratic Programming with gradient projection and Newton step projection, allowing for quicker identification of active constraints and reduced computational resources, enabling efficient real-time optimization with simple constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If nonlinear MPC is used to improve control performance, then control accuracy is improved, but computational complexity increases making real-time solution difficult
Solution Approach 1:
The patent segments the nonlinear MPC problem into multiple linear subproblems by dividing the prediction horizon into segments and applying linearization techniques to each segment. This allows the complex nonlinear optimization to be broken down into simpler linear programming problems that can be solved efficiently in real-time while maintaining control accuracy.
Solution Approach 2:
The patent transforms the nonlinear MPC formulation into a linear MPC formulation by changing the mathematical parameters and assumptions. Specifically, it uses linear approximation methods and reformulates the nonlinear optimization problem as a linear programming problem, enabling real-time solution on embedded systems while preserving essential control performance.
2Power
If standard computers are used to provide computational power, then processing capability is improved, but device size and cost increase making embedded applications impossible
Solution Approach 1:
The patent changes the computational parameters by transforming the complex nonlinear optimization into a linear programming problem with simplified constraints. This parameter transformation reduces the computational burden significantly, enabling the control algorithm to run on embedded systems with limited processing power and memory while maintaining control effectiveness.
Solution Approach 2:
The patent employs computationally efficient algorithms that can be implemented on low-cost embedded processors rather than requiring powerful standard computers. The simplified linear MPC formulation uses basic linear algebra operations that are computationally inexpensive, allowing deployment on inexpensive embedded hardware with limited resources.
3Speed
If fast sampling periods are used to improve control response, then control speed is improved, but time available for optimization decreases making real-time solution difficult
Solution Approach 1:
The patent segments the optimization problem into efficient linear subproblems that can be solved quickly. By dividing the control horizon and using incremental calculation methods, the computation time for each sampling period is significantly reduced, enabling fast sampling rates while maintaining real-time optimization capability.
Solution Approach 2:
The patent changes the computational parameters by using linear MPC formulation with simplified mathematical operations. This transformation reduces the computational complexity from nonlinear optimization to linear programming, which can be solved much faster, thereby enabling fast sampling periods with sufficient time for real-time optimization at each step.
4Device complexity
If linear approximation is used to reduce computational complexity, then computational resources are reduced, but control accuracy deteriorates
Solution Approach 1:
The patent segments the prediction horizon into multiple smaller intervals and applies linear approximation only within each small segment rather than over the entire horizon. This localized linearization maintains accuracy within each segment while keeping computational complexity low, effectively balancing accuracy and computational efficiency.
Solution Approach 2:
The patent carefully selects and adjusts the linearization parameters and model parameters to maintain control accuracy despite using linear approximation. By optimizing the linear MPC parameters and using accurate system identification, the patent achieves good control performance with reduced computational resources.
Data Source
AI summary
A method and system of predictive model control of a controlled system with one or more physical components using a model predictive control (MPC) model, determining an iterative, finite horizon optimization of a system model of the controlled system, in order to generate a manipulated value trajectory as part of a control process. At time t sampling a current state of the controlled system a cost function minimizing manipulated variables trajectories is computed with the MPC model for a relatively short time horizon in the future, wherein the MPC uses a quadratic programming (QP) algorithm to find the optimal solution, and wherein the QP algorithm is solved using an Active Sets solver (AS) class algorithm with simple constraints based on gradient projection and using Newton step projection. A move of the manipulated value trajectory is implemented and the control process is moved forward by continuing to shift the prediction horizon forward.