Deterministic Gas Turbine Control via Discrete Optimization
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Solution Overview
Problem
Existing gas turbine engine control systems face challenges with non-deterministic execution times and potential instability due to iterative algorithms used in predictive control methods, such as quadratic programming and extended Kalman filters, which can lead to sub-optimal or infeasible solutions and certification issues.
Innovation Solution
A method using a deterministic algorithm with a system model in explicit form to optimize a cost function within a guaranteed finite execution time, by restricting control variables to compatible operational constraints, ensuring feasible and optimal control actions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If iterative algorithms (quadratic programming, extended Kalman filter) are used for predictive control optimization, then control performance can be improved, but execution time becomes non-deterministic and system stability is compromised
Solution Approach 1:
The patent segments the control optimization problem into discrete time steps with a finite horizon N. By dividing the continuous optimization problem into discrete segments (time steps k, k+1, ..., k+N) and using dynamic programming, the system guarantees that each segment can be solved within a bounded computational effort, thus ensuring deterministic execution time while maintaining control performance
Solution Approach 2:
The patent implements a receding horizon control strategy where the optimization horizon N and cost function weights are dynamically adjusted based on current system state and operating conditions. This allows the controller to adapt to changing dynamics while maintaining guaranteed finite execution time through the structured discrete-time formulation
2Measurement precision
If iterative optimization algorithms are used to achieve optimal control, then control precision is improved, but the risk of sub-optimal or infeasible solutions increases due to convergence issues
Solution Approach 1:
The patent performs preliminary discretization of the state and control spaces before optimization. By pre-defining discrete state grids and control action sets, the system ensures that feasible solutions always exist within the discretized space, eliminating the risk of infeasible solutions that can occur with continuous iterative methods. The optimization then searches within this guaranteed feasible discrete space
Solution Approach 2:
The patent creates a discrete computational model (copy) of the continuous system dynamics. This discrete model mirrors the continuous system behavior but operates on finite state spaces, allowing exact optimization without convergence issues. The discrete model solutions are then mapped back to continuous control actions, ensuring both precision and feasibility
3Productivity
If complex iterative control algorithms are implemented, then control performance approaches theoretical optimum, but device complexity and certification difficulty increase
Solution Approach 1:
The patent replaces complex continuous iterative mathematical algorithms with discrete dynamic programming computations. This substitution transforms the control implementation from requiring sophisticated iterative solvers to using structured discrete computations that are more deterministic and easier to certify, while maintaining near-optimal control performance through the optimality principle of dynamic programming
Data Source
AI summary
A method of controlling a system that has a finite execution time in the optimization of a cost function:J=∑i=1NF(u(k+i|k),y(k+i|k)),where N is selected such that J is convergent; k+i is the time in the future after the passage of i time increments; u(k+i|k) and y(k+i|k) are restricted to values of the respective control variables u and performance variables y that are compatible with predetermined system operational constraints; and for each time increment i=1 . . . N, values for F(u(k+i|k), y(k+i|k)) are calculated using a system model M to determine y(k+i|k) for a plurality of respective discrete values of u(k+i|k) that are limited to and representatively sampling the range of possible values of u that are compatible with the predetermined system operational constraints, J being optimised by identifying the combination {u(k+1|k),u(k+2|k), . . . u(k+N|k)} of respective discrete values u(k+i|k) over N time increments that combination yields an optimised value for J.