Absolute stability of nonlinear control systems 2ed liao x yu p
Absolute stability of nonlinear control systems 2ed liao x yu p
... w.r.t. x n+1 : V (x) =x T Px. We x l =( n 0, ,0,− ρ ) T ,then dV dt (4.34) = x T (A T P + PA )x +(l T Px + x T Pl) f (x n+1 ), = x T (A T P + PA )x 2 ρ p n+1,n+1 x n+1 f (x n+1 ), ≤−2 ρ p n+1,n+1 x n+1 f ... (x n+1 )dx n+1 > 0forx n+1 = 0, and V (x) → +∞ as |x n+1 |→+∞. Moreover, we have dV dt (4.34) = ˙xPx + x T P x +[A T n+1 x ρ f (x...
Ngày tải lên: 01/01/2014, 17:47
Analysis and control of nonlinear process systems
... details. Example 5.2.2 (Nonlinear input–output model) Rewriting a simple nonlinear state-space model into input–output form Consider a simple nonlinear process model describing the opera- tion of a ... L 2 f h p (x 0 ) (0) L f h 1 (x 0 ) L 2 f h 1 (x 0 ) L g L f h 1 (x 0 ) L 3 f h 1 (x 0 ) . . . . . . . . . . . . L f h p (x 0 ) L 2 f h p (x 0 ) L g L f h p (x 0 ) L...
Ngày tải lên: 01/01/2014, 18:38
Tài liệu Design of Feedback Control Systems for Stable Plants with Saturating Actuators ppt
. Page 9 v= g (x) x 2 g (x) =l x 2 ~~~~~BA X 1 `X 1 Figure 3.1: Visualization of the function g (x) and the sets Pg and BA,C. Definitions of. Ily(t)llIIo< Vinputu(t) if x 0 o BA,C then Ily(t)llo, g(xo) Vinput u(t) Proof: If x 0 e BA,C, then The construction of X( t) guarantees that x( t)e
Ngày tải lên: 18/02/2014, 10:20
Motion Control Theory Needed in the Implementation of Practical Robotic Systems
... () () () 2 22 22 2 4 2 22 2 4 2 222 222 2 4 3 42 31 cos cossincossin cos cossinsin xlrl xxlxrxrxmgmrI x xrmrI xxmrgxrlx x xx xx − +−+ = −+ −+ = = = τ τ ! ! ! ! (5.1) Where θ and φ are the angles of the disk and the pendulum, respectively, as shown ... φ θ φ θ ! ! = = = = 4 3 2 1 x x x x (5.2) The parameters are: τ = torque applied to the disk, the controlling input r...
Ngày tải lên: 05/11/2013, 21:15
An Introduction to Intelligent and Autonomous Control-Chapter 5: Modeling and Design of Distributed Intelligence Systems
Ngày tải lên: 07/11/2013, 09:15
Control of continuous linear systems
... R d dx [α 1 exp (−wx) + α 2 exp (wx)] = w Ls + R (α 1 exp (−wx) − α 2 exp (wx)) = Z (α 1 exp (−wx) − α 2 exp (wx)) , where: Z = Cs + G Ls + R corresponds to the characteristic impedance of the ... 2) . Finally, the inverse Laplace transform yields the desired result: exp (At) = 1 5 2 exp (3t) + 3 exp (−2t) exp (3t) − exp (−2t) 6 exp (3t) − 6 exp (−2t) 3 exp (3t) + 2 exp (−2t) . PROBLE...
Ngày tải lên: 01/01/2014, 20:12