NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

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printed 09−Mar−2000 09:04 page 1/1 /tmp_mnt/auto/ee/willy/work/simbeam/lqr2a.mdl Integrate x1^3 Display1 Control Sequence In2 Out1 select OL/CL In1 0 Open loop 2*pi*fnat*2 s+2*pi*fnat*2 2 Limit thetadot Filter Disturbance U Disturbance Sequence defdot theta Figure 2.5: Simulink Diagram of FBS 14 def Integrate x1^2 Display LQR Controller In2 Out1 In1 0 Smart System /curtis rad −−> deg theta theta −K− thetadot Volts lqr.mat defdot input m −−> cm position To File1 def 100 lqr2a
Chapter 3 Overview of Control Strategies Implemented on the Flexible Beam System This Chapter will provide a review of all of the control strategies that were tested on the NLBP. The focus of this thesis is the comparison of the SGA method of control with a broad sample of current robust nonlinear control methodologies. Thus the following nonlinear design methodologies are included mainly to highlight the uniqueness of the SGA design method. This chapter will explain the mathemat- ical derivation of two linearized controls, a passivity based approach, abackstepping controller, and the SGA algorithm. Additionally, the details of the implementation of these controllers will be explained. 3.1 Linear Quadratic Regulation As a starting point of comparison, an H 2 optimal control was rst designed for the linearized system. With optimal control, the objective is to minimize a cost functional of the following form: V (x 0)= Z 1 (x 0 T (t)Qx(t)+u T Ru)dt (3.1) where V (x 0) represents the cost associated with moving from a given state, x 0, under a control signal u to the origin. Q and R are matrices that weight the cost of the states and the control respectively. The goal is to nd the stabilizing control signal u (x) that will minimize the cost V (x). Linear quadratic regulation has a well known solution, where the optimal stabilizing control u (x) is a simple linear combination of the states: u (x) =;Kx. K is a matrix that depends upon the input matrix B, the 15
Page 1 and 2: NONLINEAR CONTROLLER COMPARISON ON
Page 3 and 4: BRIGHAM YOUNG UNIVERSITY GRADUATE C
Page 5 and 6: ABSTRACT NONLINEAR CONTROLLER COMPA
Page 7 and 8: Contents Acknowledgments vi List of
Page 9: List of Tables 4.1 Tabular Comparis
Page 12 and 13: 4.19 SGA: Nonlinear H1 vs. Linear O
Page 14 and 15: Figure 1.1: TORA System One of the
Page 16 and 17: 1.3 Literature Review In surveying
Page 19 and 20: Chapter 2 Plant Speci cations and M
Page 21 and 22: Figure 2.2: Mechanical Model of Fle
Page 23 and 24: Figure 2.4: Translational Oscillati
Page 25: 2.3 Software Set-up All of the cont
Page 29 and 30: The optimal gain matrix was given b
Page 31 and 32: 3.3 Passivity-Based Control Certain
Page 33 and 34: limitations, k 1 and k 2 are tuning
Page 35 and 36: Now we regard as the control variab
Page 37 and 38: where V satis es the well known Ham
Page 39 and 40: ecause one can quickly adjust the Q
Page 41 and 42: Chapter 4 Simulation Results 4.1 Th
Page 43 and 44: disturbances, whereas the hardware
Page 45 and 46: Response in cm 4 3 2 1 0 −1 −2
Page 47 and 48: Response in cm Response in cm 4 3 2
Page 51 and 52: Response in cm 4 3 2 1 0 −1 −2
Page 57 and 58: It is seen in Figure 4.23 that the
Page 59: all of the physical parameters exce
Page 62 and 63: Response in m 0.05 0.04 0.03 0.02 0
Page 64 and 65: Response in m 0.05 0.04 0.03 0.02 0
Page 66 and 67: Response in m Response in m 0.05 0.
Page 72 and 73: control was that it requires only t
Page 74 and 75: to the Galerkin approximation techn
Page 77 and 78:
Bibliography [1] P. Kokotovic M. Ja
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