Linear Parameter-Varying Control
LPV control designs one controller for a family of linear models indexed by measurable parameters, guaranteeing performance across the whole operating envelope.
Systems that change shape
Many plants are linear at each operating point but change as measurable variables move: a machine whose dynamics depend on temperature, density, or magnetic field. An LPV model writes the state matrices as functions of a scheduling parameter vector theta(t) that is measured in real time but varies. The controller is likewise parameter-dependent, adapting its gains as theta moves.
Guaranteed envelope performance
Unlike ad hoc gain scheduling, which interpolates point designs and hopes, LPV synthesis proves stability and performance across the entire parameter set, including fast transitions. The design solves parameter-dependent LMIs, typically enforced at the vertices of a polytope that contains the parameter range, so a finite set of conditions covers a continuum of models.
Rate bounds
How fast theta can change matters. If theta varies arbitrarily fast, a common Lyapunov function is required, which is conservative. If the rate is bounded, a parameter-dependent Lyapunov function can be used, tightening performance. The rate bound is a genuine design input, not a nuisance.
- State matrices depend on measured scheduling parameters
- Synthesis via parameter-dependent LMIs at polytope vertices
- Guarantees hold across the whole envelope, not just points
- Parameter rate bounds trade conservatism for performance
LPV controllers are implemented by evaluating the parameter-dependent gains online as theta is measured, so the control law smoothly reconfigures itself as the operating point drifts, with no switching transients.
For a fusion machine whose plasma response changes across a discharge, an LPV formulation would let a single certified controller cover the ramp, flat-top, and ramp-down phases, scheduled on measured plasma parameters. Such designs for the Hyperion configuration would be simulation studies, since the machine is not built. LPV is the rigorous successor to classical gain scheduling.