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Path: Common/Control
% Implements a phase plane controller.
The optimality condition is
J = T + k*integral[0,T]( |u| dt )
where u is the control and T is the final time.
The solution consists of two switching curves. When k is inf you
get the time-optimal solution with one switching curve. If k > 0
you will get two switching curves. The former is known as a
"bang-bang" controller and the latter a "bang-zero-bang" controller.
The deadband separates the switching curves at the origin by db.
The rate limit sets u = 0 if the state is within the control.
Type PhasePlane for a demo.
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Form:
u = PhasePlane( v, x, k, db, rl )
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Inputs
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v (1,1) Rate
x (1,1) Position
k (1,1) Weight on time
db (1,1) Deadband
rl (1,1) Rate limit
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Outputs
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u (1,1) Control [-1;0;1]
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Reference: Athans, M. and P. L. Falb. (1966.) Optimal Control
Lincoln Laboratory Publication.
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