Final results

[BystrickyK]

Task -> Control heating/cooling elements on a plate to create a heat image according to the reference image
In the following animations, the reference is set by this image

The plate is discretized into 50x50 nodes. Each 6th node is an input node and can input or extract heat from the node.

In each simulation step, there's a chance that a 3x3 square with random coordinates will spontaneously cool down by -5. This is to demonstrate the controller's ability to deal with unexpected disturbances.

Unconstrained LQ-MPC regulation, large steady-state error:

B_unconstrained_LQ.mp4

Unconstrained LQ-MPC reference tracking with a system augmented with an input integrator, and the controller output defined as the change in system input (rather than the system input directly).

B_unconstrained_dU_reftracking.mp4

LQ-MPC, ref tracking, system with input integrator. Control sequence computed using quadprog, with asymetric bounds on deltaU (positive deltas can be larger than negative deltas).

LQMPC_deltaU_quadprog.mp4

[BystrickyK]

118x118 grid, reference image
The state dimension rises rapidly with the size of the image. All matrices had to be defined as sparse matrices for both time and memory purposes.

LQ-MPC, ref tracking, delta U input, unbounded
https://user-images.githubusercontent.com/55796835/119216472-2dd99780-bad4-11eb-88a6-29e25a76a7b4.mp4

Bounded, asymmetric bounds, computed using quadprog. Each computation took ~ 1.8 seconds, much longer than the previous unconstrained case.

cvut_du_reftrack_bounded_quadprog.mp4