Controlled/manipulated variable selection: setpoint tracking, full SVD, reachable ellipsoid, Matlab (2)

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 14:09

*Enlace a Spanish version

Summary:

This video continues the case study that began in the video [sacerf1EN], which discussed the problem statement of selection/sizing of manipulated and controlled variables for setpoint tracking tasks.

In said video, minimum gain and conditioning were scaled and checked. In this video we will discuss additional concepts such as:

• Complete U,S,V analysis of the SVD decomposition. Easy and difficult maneuvers in input and output directions are analysed; the null space of the gain matrix is also pinpointed (direction of $u$ without effect in steady state increment).

• Since the nullspace is highly aligned with actuator 2, the analysis is repeated assuming that actuator 2 is not incremented; It is verified that the gains and conditioning barely change, so the setpoint tracking problem continues to be feasible.

• The reachable output ellipsoid achievable with the unit sphere in actuators, as well as the circle of radius 1 and the circle of minimum gain, are graphically represented in the (scaled) output domain. It is verified that, since the minimum gain is $\ge \sqrt{2}$ then the input unit sphere sweeps all the square of vertices $\pm 1$ in the output domain, guaranteeing the feasibility of the problem with geometry of polyhedra (which will be discussed in depth in the video [sacerf3EN], a continuation of this case study).

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.