This paper presents a basic example of PID control applied to a robotic manipulator arm with two DOF (degrees of freedom), as well as the design of th...
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In this paper a PID controller for a universal motor, place to see how this type of controllers, the simplest being can reach control system optimally, based on the parameters as designer want obta...
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•
θ (t) = f (τ (t))
• τ (t) = g (θ (t))
K E E P E E
F =
d (mv ) dt
d T = I ω = I ω˙ + ω × (I ω) dt
d2 θ ⇒ dt2 τ = M L2 θ¨ + MgLcosθ
L(q (t), q ˙(t)) = K E ˙(t)) − P E E (q (t), q E (q (t)) L
d F = dt
τ − MgLcosθ = I
∂ L ∂ L − ∂ θ˙ ∂ θ
F
θ
L
K E E = m
1 mv 2 2 v
P E E = mgl g
l F
K E E =
1 ˙2 I θ 2 I = M L2
I
t
F = K p e + K i
P E E = M gh = MgLsenθ
e(τ )dτ + K d e˙
0
e = q d − q q d
K p K i
K d
L(q (t), q ˙(t)) = K E ˙(t)) − P E E (q (t), q E (q (t)) 1 L(q (t), q ˙(t)) = M L2 θ˙2 − MgLsenθ 2
F = K p e + K d e˙ + ξ ξ ˙ = K i e, ξ (0) (0) = ξ 0
∂ L = −MgLcosθ ∂θ ∂ L = M L2 θ˙ ˙ ∂ θ d ∂ L = M L2 θ¨ ˙ dt ∂ θ
F
M (q )¨ q + C (q, q ˙) + g (q ) = K p e + K d e˙ + ξ )¨q
F = M L2 θ¨ + MgLcosθ
F = M (q )¨ )¨q q + C (q, q ˙) + g(q )
ξ e e˙
n
M (q ) ˙ C (q, (q )) )) = {ckj } ∈ Rnxn g(q ) F ∈ R
n
T
ξ T eT e˙T
d dt
q ∈ Rn
ξ ˙ = K i e
ξ
e e˙ 1 d q − M (q ) [K p e + K d e˙ + K i ξ −C (q, q ˙)q ˙ − g(q )
