Aircraft Actuator Allocation Using Null-Space Task Separation
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Solution Overview
Problem
Existing control methods for overdetermined systems with multiple actuators, such as aircraft, struggle to manage primary and non-primary tasks simultaneously without affecting the stability and performance of the primary task, as secondary or tertiary tasks can negatively impact the solution of high-priority goals.
Innovation Solution
A method involving a control unit that determines a pseudo-control command based on a physical model, calculates a control matrix to manage primary tasks, projects non-primary tasks into the null space of the primary task to avoid interference, and provides overall control commands to the actuators, ensuring that low-priority tasks do not adversely affect high-priority tasks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If secondary or tertiary tasks are added to the control and allocation problem, then the system can perform additional non-primary tasks, but the available performance for solving primary tasks and the stability of the solution deteriorates
Solution Approach 1:
The control task is segmented into primary and non-primary components. The primary task control command is calculated first, then the non-primary task is projected into the null space of the primary task's control matrix, ensuring independent optimization without interference between task priorities
Solution Approach 2:
The non-primary task is transformed from the original control space into the null space dimension, which is orthogonal to the primary task's control direction. This dimensional transformation allows the non-primary task to be executed without affecting the primary task's solution stability
2Adaptability or versatility
If multiple tasks with different priorities are combined in one control step, then the system can handle diverse objectives, but the ability to assign different priorities and criticalities to different goals deteriorates
Solution Approach 1:
The control algorithm is segmented into distinct stages: first calculating the primary task control command, then separately projecting and adding the non-primary task component. This segmentation enables clear priority assignment where primary tasks are always satisfied first, followed by non-primary tasks in the null space
Solution Approach 2:
The null space projection acts as an intermediary mechanism that mediates between primary and non-primary tasks. It transforms the non-primary task into a form that does not conflict with the primary task, allowing both to coexist with properly assigned priorities
3Adaptability or versatility
If secondary goals are achieved with lower criticality, then the system can optimize for additional objectives, but failure or erroneous behavior in secondary goals can negatively affect primary goals
Solution Approach 1:
The non-primary task is extracted from the main control problem and projected into the null space of the primary task's control matrix. This extraction ensures that the non-primary task operates independently in a subspace that does not affect the primary task's solution, eliminating the risk of erroneous behavior in secondary goals impacting primary goals
Data Source
AI summary
A method for controlling an overdetermined system with multiple actuators, for example an aircraft (1) with multiple propulsion units (3). The actuators perform at least one primary task and at least one non-primary task, including: a) determining a pseudo-control command up∈p′ based on a physical model of the system, which command represents the torques (L, M, N) and a total thrust force (F) acting on the system, b) determining a control matrix D, D∈p′×k according to up=Du, where u1=D−1upu1∈k represents a control command for the actuators to perform the primary task, c) projecting the non-primary task into the null space N(D) of the primary task, so that Du2=0 if u2u2∈k represents a control command for the actuators to perform the non-primary task, and d) providing the control commands from b) and c) to the actuators. In this way, the solution of the primary task is not adversely affected by the non-primary task or its solution.