Nonlinear control of electrical flexible-joint robots
Citations
103 citations
97 citations
68 citations
Cites background from "Nonlinear control of electrical fle..."
...…control is one of the most important points in designing a controller for industrial systems, because if the computational burden of the controller is high, owing to delay in online control, the stability of the closed- loop system cannot be guaranteed (Soltanpour and Fateh, 2009; Fateh, 2012a)....
[...]
59 citations
58 citations
Cites background from "Nonlinear control of electrical fle..."
...According to (30), we have Ia = K−1m ( Jmr−1q̈ + Bmr−1q̇ + r (Dq̈ + Cq̇ + G) ) (52) Using (52) and its time derivative, the lumped uncertainty F(t) in (18) can be rewritten as F(t) = F1(q)̇q̈ + F2(q, q̇)q̈ + F3(q, q̇)q̇ + F4(q, q̇) (53) where F1(q) = LK−1m rD(q) and F2(q, q̇) = RK−1m ( Jmr−1 + rD ) + LK−1m (Bmr−1 + rḊ + rC) + Kbr−1 − In (54) F3(q, q̇) = RK−1m ( Bmr−1 + rC(q, q̇) ) + LK−1m rĊ(q, q̇) (55) F4(q, q̇) = RK−1m rG(q) + LK−1m rĠ(q, q̇) (56) According to the stability analysis, in the sinusoidal steady state, the joint position q and its time derivatives converge to their desired trajectories....
[...]
...Substituting (37) into (36) and some simple manipulations yields V̇ ≤ −q̃T Kpq̃ + ∥∥q̃T E∥∥ λe−δt ‖y‖ + λe−δt (38) Using the inequality ab a+b < a ∀a, b > 0, (38) can be rewritten as V̇ ≤ −q̃T Kpq̃ + λe−δt (39) According to Qu et al.,1 (39) implies that q̃ asymptotically converges to zero and P̃ is bounded....
[...]
...V (t) = q̃ T q̃ 2 + P̃ T P̃ 2γ (32) The time derivative of (32) given by V̇ (t) = q̃T ˙̃q − P̃ T ˙̂P γ (33) Substituting ˙̃q from (29) into (33) yields V̇ = q̃T (−Kpq̃ + ξ P̃ + ε − Fr) − P̃ T ˙̂P γ (34) Using (31), we can simplify (34) as V̇ = q̃T (−Kpq̃ + ε − Fr) (35) It follows from (35) and Assumption 3 that V̇ ≤ −q̃T Kpq̃ + ∥∥q̃T E∥∥ − q̃T Fr (36) According to Qu et al.,1 we can propose the robustifying control term Fr as Fr = yE‖y‖ + λe−δt (37) in which λ and δ are positive scalars and y = Eq̃....
[...]
...Using (9)–(13), the state-space model is obtained ẋ = F(x)+bv (14) in which x = [q q̇ Ia ]T , b = [0 0 L−1 ]T (15) F(x) = ⎡ ⎣ x2(Jr−1 + rD(x1))−1(−(Br−1 + rC(x1, x2))x2 − rG(x1) + Kmx3) −L−1(Kbr−1x2 + Rx3) ⎤ ⎦ (16)...
[...]
...Using Assumption 1, bounded-ness of the control law (27) is obtained....
[...]
References
1,542 citations
"Nonlinear control of electrical fle..." refers background or methods in this paper
...To simplify (42), we use a property of robot dynamics [ 7 ] that...
[...]
...However, a simplified model was provided that under some assumptions is being feedback linearized [ 7 ]....
[...]
...The vector of the gravitational torques g(θ ) is assumed to be a function of only the joint positions as used in the simplified model [ 7 ]....
[...]
...In a simplified model of flexible-joint robot [ 7 ], the links of manipulator are assumed rigid and the motors are elastically coupled to the links....
[...]
...For instance, PD control [3], robust control using voltage control strategy [4], integral manifold approach [5], singular perturbation theory [6], robust control [ 7 ], sliding mode control [8], adaptive control [9], adaptive neural network control [10], fuzzy control [11], learning control [12], neural network approach [13], passivity-based impedance control [14], and state observer based control [15] have been devoted to dealing with the ......
[...]
539 citations
"Nonlinear control of electrical fle..." refers background in this paper
...For instance, PD control [ 3 ], robust control using voltage control strategy [4], integral manifold approach [5], singular perturbation theory [6], robust control [7], sliding mode control [8], adaptive control [9], adaptive neural network control [10], fuzzy control [11], learning control [12], neural network approach [13], passivity-based impedance control [14], and state observer based control [15] have been devoted to dealing with the ......
[...]
...Generally, a flexible-joint robot cannot be feedback linearized by static feedback [ 3 ]....
[...]
444 citations
"Nonlinear control of electrical fle..." refers methods in this paper
...For instance, PD control [3], robust control using voltage control strategy [4], integral manifold approach [ 5 ], singular perturbation theory [6], robust control [7], sliding mode control [8], adaptive control [9], adaptive neural network control [10], fuzzy control [11], learning control [12], neural network approach [13], passivity-based impedance control [14], and state observer based control [15] have been devoted to dealing with the ......
[...]
424 citations