Commercial insecticides are widely used in most sectors of the agricultural production to avoid or reduce losses by insects and hence it can improve the production as well as the quality of the product produced. In some ways, it can also improve the value of food and also its safety. Insecticides can be considered as an economic, labour-saving and efficient tool of insect management in agricultural production [1]

Abdul Halim, Norhazimah

Abdullah, Dzul Izlee

Amri, Muhammad Akmal

Mohd Noor, Siti Fatimah

Muhamad, Aida

Shaari Majed, Muhammad Amer Daneal

English

UTHM Institutional Repository

Proceedings of International Conference on Mechanical & Manufacturing Engineering (ICME2008), 21– 23 May 2008, Johor Bahru, Malaysia.  © Faculty of Mechanical & Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Malaysia.  ISBN: 97–98 –2963–59–2  Response Analysis of UTHM’s Airship    Azian Hariri1,*, Darwin Sebayang2, **, Ignatius Agung Wibowo3, *** 1, 2 Faculty of Mechanical and Manufacturing Engineering  Tun Hussein Onn University of Malaysia (UTHM) Parit Raja, Batu Pahat, 86400 Johor Malaysia  3 Faculty of Electrical and Electronics Engineering  Tun Hussein Onn University of Malaysia (UTHM) Parit Raja, Batu Pahat, 86400 Johor Malaysia  *azian@uthm.edu.my **darwin@uthm.edu.my ***agung@uthm.edu.my    Abstract: Response of airship owing to deflection angle of elevator, rudder and vectored thrust during trimmed equilibrium flight can be computed by solving the airship equations of motion. In this study, the linearised decoupled airship equations of motion were used and the solution was computed with the aid of Matlab software. This paper shows a case study done by applying the physical data of a designed airship called ‘UTHM’s Airship’ in the equations of motion and solved it in order to understand and analyze the response of the designed airship. For ‘UTHM’s Airship’, the longitudinal response of elevator and thrust vectorization has relatively low longitudinal control power and a rather sluggish response characteristic. Meanwhile the lateral response of rudder demonstrates a relatively high rudder control power and quicker lateral response compared to longitudinal response. The results had successfully given an initial insight of the ‘UTHM’s Airship’ response and dynamic stability.  1. Nomencleature a - State matrix a - Coordinate centre of gravity b - Input matrix B - Buoyancy force g - Gravitational constant J  - Moment of inertia  L - Rolling moment M - Pitching moment m - Mass matrix m - Airship mass N - Yawing moment p - Roll rate perturbation q - Pitch rate perturbation r - Yaw rate perturbation U - Axial velocity u - Input or control vector u - Axial velocity perturbation v - Lateral velocity perturbation W - Normal velocity w - Normal velocity perturbation X - Axial force  1Proceedings of International Conference on Mechanical & Manufacturing Engineering (ICME2008), 21– 23 May 2008, Johor Bahru, Malaysia.  © Faculty of Mechanical & Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Malaysia.  ISBN: 97–98 –2963–59–2  x - State vector Y - Lateral force Z - Normal force  Greek Letter β  - Sideslip angle δ  - Control angle θ  - Pitch attitude φ  - Roll attitude ψ  - Yaw attitude  Subscripts a - Aerodynamic e - Trim equilibrium ele - Elevator p - Roll rate q - Pitch rate r - Yaw rate rud - Rudder δ  - Control angle u - Axial velocity V0 - Total velocity v - Lateral velocity w - Normal velocity x - Body axis reference y - Body axis reference z - Body axis reference  Examples of Notation Dimensional derivatives denoted thus     qMM qo∂∂=   etc.  2. Introduction An airship is a lighter than air vehicle which produces the significant lift due to aerostatic effect or buoyancy force. It is basically an aircraft that derives its lift from a lifting gas usually helium while it is propelled forward by an engine. It differs from the conventional aircraft in terms of lift producing mechanism. The potential of the airship can be realized in terms of less fuel consumption, high endurance, and ability to hover. One of the crucial subjects of airship is stability. An airship is considered stable if the response approaches zero as time approaches infinity. Thus, through response output, the stability of the airship can also be determined. The response of airship can be computed by solving the airship equations of motion.  Although the airship equations of motion had been discussed by previous researchers [1-4], the true challenge is actually to develop the overall programming code from scratch since none of the programming codes were reveals in any literatures. This paper shows a case study done by applying the physical data of a designed airship called ‘UTHM’s Airship’ in the equations of motion and solved it in order to understand and analyze the response of the designed airship.  3. Airship Equations of Motion Equations of motion are equations that describe the behavior of system. Equations of motion of airship was based on Newton’s second law of motion which simply states that mass times acceleration equal to disturbing force. For the rotary degree of freedom, moment of inertia times angular acceleration equal to disturbing moment. The disturbing force and moment of the designed airship were due to the aerodynamic effects, thrust effects, gravitational effects, buoyancy effects, coriolis effects and centrifugal effects when disturbed from its equilibrium state [1-4].  The responses owing to control inputs are obtained from the non linear equations of motion during the initial condition of trimmed equilibrium flight. These non linear equations of motion is linearised by constraining about small perturbation condition and restricted to the chosen designed cruising speed. Since only small perturbation is consider, it is convenient to simplify the equations by  2Proceedings of International Conference on Mechanical & Manufacturing Engineering (ICME2008), 21– 23 May 2008, Johor Bahru, Malaysia.  © Faculty of Mechanical & Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Malaysia.  ISBN: 97–98 –2963–59–2  assuming that longitudinal and lateral motion is decoupled [1-4]. The linearised decoupled equations were then converted to state space form for the convenience of computing the transfer function and response of the designed airship.   3.1 Linearised Decoupled Equations of Motion The linearised longitudinal decoupled equations of motion describing small perturbations about the trim state follow when the trim terms, which sum to zero, are removed. It may be written in state space form as below [1-4, 7].      [ ][ ]teleTT qwuδδθ==ux⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡⎟⎠⎞⎜⎝⎛ +−⎟⎠⎞⎜⎝⎛ −⎟⎟⎠⎞⎜⎜⎝⎛ +−⎟⎟⎠⎞⎜⎜⎝⎛ −=10000mama0mam00ma0m....yowxouzoqxzoqzxJMMZXm( ) ( ) }{⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡−−−−−−−−=⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡=0100sinamcosammama00sin)m(m0cos)m(m000000000exezezexaeexaeezattggWUMBgUZBgWXMMZXXθθθθδδδab(1)   The linearised lateral equations of motion may be developed similarly as below [1-4, 7].  [ ][ ]rudTT rpvδφ==ux  ⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡−⎟⎠⎞⎜⎝⎛ −−⎟⎠⎞⎜⎝⎛ +−⎟⎠⎞⎜⎝⎛ −⎟⎟⎠⎞⎜⎜⎝⎛ +−=10000ma0ma0mama....zxzovxxzxovzorxopzyJJNJJLYYmm ⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡−−−−−=⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡=0010cos)am(mama0cos)am(mama0cos)m(mm0000exexaexezezezaeexezagUNWgUWLBgUWYNYθθθδδab  (2)                                                        In lateral perturbation, the sideslip angle β is given by [2] 0tanVv=≅ ββ  (3) Since ψβ −= , yaw angle is given by 0Vv−=−= βψ  (4) In order to incorporate yaw angles, in the output equations, the lateral perturbation equations can be modified as follows [2].        [ ]⎥⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎢⎣⎡−==000110000100001000010VrpvTCx ψφ      (5) ⎥⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎢⎣⎡=00000D   4. Solution of the Equations of Motion The process of solution requires the numerical values for the derivatives and other parameters are substituted and then the whole model is input to a suitable computer program. The output, which obtained instantaneously, is most conveniently arranged in terms of response transfer functions. Time step for the airship response to control can be obtained by finding the inverse Laplace transform of the appropriate transfer function expression. The solution of equations of motion can painlessly be achieved with the aid of Matlab software.  3Proceedings of International Conference on Mechanical & Manufacturing Engineering (ICME2008), 21– 23 May 2008, Johor Bahru, Malaysia.  © Faculty of Mechanical & Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Malaysia.  ISBN: 97–98 –2963–59–2  6. Results and Discussion Due to limited pages in this paper, the programming codes are not shown here. From the Matlab programming conducted, the longitudinal response to elevator is shown on Figure 2 which the input is a 1 degree elevator step.  5. Case Study: UTHM’s Airship  UTHM’s Airship is a remotely control non-rigid airship for aerial monitoring purposes. The basic specifications of the designed airship are as outlined in Table 1 below.  -0.200.2From: elevatorTo: u (m/s)00.050.1To: w (m/s)-505x 10-3To: q (rad/s)0 10 20 30 40 50 60 70 80 90 10000.010.02To: pitch angle (rad)Step ResponseTime (sec)Amplitude Table 1: Basic specifications of UTHM’s Airship Specifications Flight performance Min. Payload 8 kg Max. speed 40 km/h Cruising speed 20 km/h Operating altitude 120 meter Envelope Shape Ellipsoid + cylinder Length 10m Max. diameter 2.3m  Figure 2: Longitudinal response owing to 1 degree elevator input  Volume Approx. 30 m3 The magnitudes of the response variables are very small and the time taken for the transient to settle down is in order of approximately 80 seconds. Although it is longitudinally stable, it also clearly demonstrates a relatively low longitudinal control power and a rather sluggish response characteristic. The airship envelope consists of ellipsoidal shape for nose and tail section, and cylinder for the middle section. The designed airship was equipped with vectored thrust system moving in vertical direction from -45 to 70 degree measured positive angle of thrust line up from the horizontal. For elevators and rudders, the control is from -30 to 30 degree measured positive of elevator deflection upward and rudder deflection to left as if the pilot of the airship. The preliminary dimensions of the designed airship are shown in Figure 1 below [5-6]. The longitudinal response to a 1 degree step in thrust is shown on Figure 3.    024x 10-4 From: thrustTo: u (m/s)-505x 10-5To: w (m/s)-505x 10-6To: q (rad/s)0 10 20 30 40 50 60 70 80 90 100024x 10-5To: pitch angle (rad)Step ResponseTime (sec)AmplitudeFigure 1: Preliminary dimension of UTHM’s Airship                                                                                                                                   Figure 3: Longitudinal response owing to 1 degree thrust input  Diameter 2.3 m 9.07 m 5.00 m3.47 m cv 3.60 m0.53 m10.00  4Proceedings of International Conference on Mechanical & Manufacturing Engineering (ICME2008), 21– 23 May 2008, Johor Bahru, Malaysia.  © Faculty of Mechanical & Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Malaysia.  ISBN: 97–98 –2963–59–2  It is clear that, although the engines are mounted below the centre of gravity, the pitch response to a thrust change is very small. The only significant response is in axial velocity perturbation, u as might be expected. Again the general magnitude is small and time scale of response is approximately 80 seconds. This confirms although it is longitudinally stable, the longitudinal control power is low and response is sluggish.  The lateral response to a 1 degree step command input to rudder is shown onFigure 4.   -0.04-0.020To: v (m/s)-505x 10-3To: p (rad/s)00.0050.01To: r (rad/s)-505x 10-3To: roll  (rad)0 10 20 30 40 50 60 70 80 90 10000.0050.01To: yaw  (rad)Step ResponseTime (sec)Amplitude Figure 4: Lateral response owing to 1 degree rudder input  The significant response magnitudes are for lateral velocity perturbation, v. It is clear that rudder control power is low. However, the transient settle in approximately 50 seconds, indicating a quicker lateral response than longitudinal response and a stable lateral motion.  7. Conclusion UTHM’s Airship is dynamically stable during designed cruising speed of 20km/h with time taken for the transient to settle down is in order of 80 seconds for longitudinal and 50 second for lateral response. Although the response shows a stable airship, the open loop responses of the airship are sluggish with very low control power. Thus this indicated the need of designing a control system to enhance the response of the airship.  5. References [1]G.A. Khoury and J.D. Gillet, Airship Technology, Cambridge University Press, United Kingdom 1999. [2]M.V.Cook, Flight Dynamics Principles, Butterworth Heineman, Oxford, United Kingdom 1997.            [3] J.B. Mueller, M.A. Paluszek and Yiyuan Zhao, Proceedings of the AIAA 3rd Unmanned Unlimited Technical Conference, Workshop and Exhibit, Chicago, U.S September 2004.    [4]S.B.V. Gomes and J.J.G. Ramos, Proceeding of the 1998   IEEE International Conference on Robotics & Automation, Leuven, Belgium, May 1998, pp. 3462-3467.    [5] Azian Hariri, Darwin Sebayang, Ignatius Agung Wibowo, Mohamad Zainal Md. Yusof and Sugiarmadji Hari Purnama Singgih, Proceeding National Conference on Design & Concurrent Engineering 2006, Melaka, Malaysia, August 2006.    [6] Darwin Sebayang, Mohamad Zainal Md. Yusof, Azian Hariri, Ignatius Agung Wibowo, Sugiarmadji Hari Purnama Singgih, Proceeding Malaysian Technical Universities Conference on Engineering and Technology (MUCET), Batu Pahat, Johor, Malaysia, December 2006, pp.324-331.    [7] Azian Hariri, Darwin Sebayang, Ignatius Agung Wibowo, Mohamad Zainal Md. Yusof, Proceeding of Mechanical and Aerospace Engineering Conference, World Engineering Congress (WEC2007), Penang, Malaysia, August 2007, pp.136-153.      5

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