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This PR adds some new functionality for I/O systems that I used in a recent course on optimization-based control that I taught at Caltech:
Modify the
ss()
,rss()
, anddrss()
functions to returnLinearIOSystem
objects (instead ofStateSpace
objects). This makes it easier to create LTI state space systems that can be combined with other I/O systems without having to add a conversation step. SinceLinearIOSystem
objects are alsoStateSpace
objects, no functionality is lost. (This change is implemented through the introduction of a internalNamedIOSystem
class, to avoid import cycles.)Added a new function
create_statefbk_iosystem()
that creates an I/O system for implementing a linear state feedback controller of the form u = ud - Kp(x - xd). The function returns an I/O system that takes xd, ud, and x as inputs and generates u as an output. Theintegral_action
keyword can be used to define a set of outputs y = C x for which integral feedback is also included: u = ud - Kp(x - xd) - Ki(C x - C xd).The
lqr
anddlqr
commands now accept anintegral_action
keyword that allows outputs to be specified for implementing integral action. The resulting gain matrix has the form K = [Kp, Ki]. (This is useful for combining with theintegral_action
functionality increate_statefbk_iosystem()
).