Roll Model Research Method 1. The Augmented Plant

 ISSN: 1693-6930 TELKOMNIKA Vol. 14, No. 3, September 2016 : 963 – 973 968 des x ref t f x errorx x u u y θ θ θ           +                 +                               = 1 1 1 1   22 And then it is converted back into continuous-time state space form. ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ � ̇ �̈ �̇ �̈ �̇ ����� � ̇ ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 0.0006546 1 −28.37 −1.984 −0.002709 −0.00452 −0.03731 0.958 −1.191 −0.09954 −3.892 −5.36 −0.003059 0.0001403 0.9915 −0.1128 0.003059 −0.0001403 −0.9915 0.1128 −80.59 −80.59⎦ ⎥ ⎥ ⎥ ⎥ ⎤ ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ � �̇ � �̇ � ����� �⎦ ⎥ ⎥ ⎥ ⎥ ⎤ + ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 80.59 0⎦ ⎥ ⎥ ⎥ ⎥ ⎤ � � ��� �� � + ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ −0.001305 55.65 −0.02015 −0.1318 0.0008007 −0.0008007⎦ ⎥ ⎥ ⎥ ⎥ ⎤ � ��� 23 des x ref f x errorx x u u y θ θ θ           +                 +                               = 1 1 1 1   24

2.3. Roll Model

In a similar way, the roll model is obtained in the form of transfer function and state space as follows: 30 235 . 3 28 . 68 2 2 2 2 2 + + = + + = s s s s k s s n n n des ω ζω ω ϕ ϕ 25 Where � : actual roll degree � ��� : roll input value to the drone degree Furthermore, it is converted into continuous-time state space form 26, 27 and discrete-time state space with sampling time ∆t 0.2 s 28, 29. des ϕ ϕ ϕ ϕ ϕ       +             − − =       28 . 68 235 . 3 30 1     26 [ ]       = ϕ ϕ  1 y 27 TELKOMNIKA ISSN: 1693-6930  H-INFINITY Control for Pitch-Roll AR.DRONE Agung Prayitno 969 des t t ϕ ϕ ϕ ϕ ϕ       +             − =       + 174 . 8 011 . 1 1686 . 591 . 3 1197 . 558 . 1   28 [ ] t y       = ϕ ϕ  1 29 Where � : actual roll degree �̇ : sideward speed degreesecond And it will be obtained the state space sideward velocity and sideward acceleration as follows: 1 1 1082 . 0245 . 5123 . 394 . 0814 . 9195 . + +       +             − =       t t t v v v v ϕ   30 [ ] t v v y       =  1 1 31 Where � : sideward velocity metresecond �̇ : sideward acceleration metresecond 2 Equation for y-position and error y based on data from the AR.Drone. t v y y t t t ∆ + = +1 32 t ref y y errory − = 33 Furthermore, equations 28, 29, 30, 31, 32, and 33 are combined to form a state space which represents a model of the AR.Drone roll system. des y ref t t f y errory y v v errory y v v ϕ ϕ ϕ ϕ ϕ                     +                           +                                         − − − − =                     + 1094 . 0248 . 174 . 8 011 . 1 1 1 2 . 1 2 . 5123 . 394 . 013 . 0601 . 0814 . 9195 . 0029 . 0136 . 1686 . 591 . 3 1197 . 5558 . 1     34 des y ref t f y errory y v v y ϕ ϕ ϕ           +                 +                               = 1 1 1 1   35 And then it is converted back into continuous-time state space form.  ISSN: 1693-6930 TELKOMNIKA Vol. 14, No. 3, September 2016 : 963 – 973 970 ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ �̇ �̈ �̇ �̈ �̇ ����� � ̇ ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ = ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ −0.0005242 0.9999 −30 −3.235 0.07753 0.008759 −0.2865 0.572 0.7104 0.06255 −2.769 −3.148 −0.007378 −0.0005951 1.024 −0.06372 0.007378 0.0005951 −1.024 0.06372 −80.59 −80.59⎦ ⎥ ⎥ ⎥ ⎥ ⎤ ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ � �̇ � �̇ � ����� �⎦ ⎥ ⎥ ⎥ ⎥ ⎤ + ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 80.59 0⎦ ⎥ ⎥ ⎥ ⎥ ⎤ � � ��� �� � + ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 0.0007055 68.28 0.03046 0.1214 −0.0008061 0.0008061 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ � ��� 36 des y ref f y errory y v v y ϕ ϕ ϕ           +                 +                               = 1 1 1 1   37

2.4. Calculating K value