Control Allocation
Control allocation distributes a commanded virtual control among redundant actuators, respecting their limits and secondary objectives.
Redundant actuation
Many systems have more actuators than degrees of freedom to control: an aircraft with multiple control surfaces, a vehicle with several thrusters, or a machine with many independently driven coils. A high-level controller computes the total effect required, the virtual control, and control allocation decides how to split that demand across the physical actuators. This modularity separates the control law from the actuator geometry.
The allocation problem
Mathematically, allocation solves for actuator commands u such that the effectiveness matrix B times u equals the virtual command, subject to actuator position and rate limits. Because B has more columns than rows, the solution is underdetermined, and the freedom is used to meet secondary objectives, such as minimizing actuator effort, wear, or a weighted norm. When the demand exceeds actuator capacity, the allocator finds the achievable command closest to the desired one.
Methods
Simple pseudoinverse allocation minimizes the two-norm of u but ignores limits. Constrained methods, such as quadratic-programming allocation or the redistributed pseudoinverse, honor saturation by solving a small optimization each step. Daisy-chaining prioritizes actuators in tiers, using secondary ones only when primary ones saturate. Direct allocation preserves the direction of the commanded effect even under saturation.
- Split a virtual command among redundant actuators
- Underdetermined: extra freedom meets secondary goals
- Constrained solvers honor position and rate limits
- Saturation handled by QP, daisy-chaining, or direct allocation
Keeping allocation separate from the control law means the controller need not know actuator details, and reconfiguration after an actuator failure becomes an allocation update rather than a controller redesign, a key benefit for fault tolerance.
For a design-stage machine with many coils or actuators sharing a control task, allocation would translate the controller's high-level demand into per-actuator commands within limits, evaluated in simulation. It complements MPC and other high-level schemes.