DESIGNING AND IMPLEMENTATION OF AN OPTIMIZED PID CONTROLLER FOR LONGITUDINAL AUTOPILOT

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Advance Research Journal of Multi-Disciplinary Discoveries ISSN NO : 456-145 DESIGNING AND IMPLEMENTATION OF AN OPTIMIZED PID ONTROLLER FOR LONGITUDINAL AUTOPILOT Original Research Article ISSN ODE:

Website: wwwjournalresearchijfcom Received: 6317 Accepted: 5317 Date of Publication: 5-4-17 Page: 1-6 ABSTRAT This paper presents the design of an Aircraft model for Longitudinal Dynamics We

1 Advance Research Journal of Multi-Disciplinary Discoveries ISSN NO : DESIGNING AND IMPLEMENTATION OF AN OPTIMIZED PID ONTROLLER FOR LONGITUDINAL AUTOPILOT Original Research Article ISSN ODE: (Online (IV-EE/Impact Value: 38 (GIF Impact Factor: 174 opyright@ijf 17 Journal ode: ARJMD/EE/V-11/I-1/-5/MARH-17 ategory : ELETRIAL ENGINEERING Volume : 11 / hapter- V / Issue -1 (MARH Website: wwwjournalresearchijfcom Received: 6317 Accepted: 5317 Date of Publication: Page: 1-6 ABSTRAT This paper presents the design of an Aircraft model for Longitudinal Dynamics We formulated a design of inner and outer loop of an aircraft with and without optimization (PID controller for continuous and discrete controller by controlling the variables of an aircraft using a simulation loop of a MATLAB The different flight conditions were arrived using Orthogonal Array (OA based on different Aircraft weight, Altitude, Mach number configurations This attempts to span the aircrafts across the regimes in aircrafts flight envelope Performance against uncertainties also included like turbulence and variation of atmospheric conditions Index Terms : Attitude control, Aircraft navigation, PID controller, Discrete optimization, Pitch Attitude Hold Mode Name of the Author: Princy Randhawa Assistant Professor, Department of Mechatronics Engineering School of Automobile,Mechanical and Mechatronics Engineering, Manipal University Jaipur,Rajasthan (INDIA itation of the Article Randhawa P (17, March Designing and Implementation of an Optimized PID ontroller for Longitudinal Autopilot, Advance Research Journal of Multidisciplinary Discoveries11,- 5(17:1-6 ISSN An open access journal of International Journal Foundation wwwjournalresearchijfcom Page I 1

2 Advance Research Journal of Multi-Disciplinary Discoveries ISSN NO : I INTRODUTION An autopilot is a system used to control the trajectory of an aircraft without constant 'hands-on' control by a human operator being required The first aircraft autopilot was developed by Sperry orporation in 191The main aim of the autopilot is to track the desired goal There are several various control techniques available for the design of an autopilot like Frequency domain techniques: Root Locus, Bode Plot, Nyquist Plot, PID Design and for Time domain Techniques: Pole Place ment Technique, Eigen Structure Assignment, Optimal ontrol (LQR Design and Advance Techniques like Robust ontrol, Sliding Mode ontrol, Adaptive ontrol etc [] Every Technique has its advantages and Disadvantages so as to improve its performance new techniques has proposed In this paper presents the simplest technique using optimized PID controller for determining the stability of the modes of the autopilot In control law design there are thousands of different sets and combinations of altitude, velocity, etc In this we discuss about the method known as orthogonal array to reduce the no of sets II ONTROL LAW DESIGN OF AN AIRRAFT Xu Zu A n = u M u I n = B n= 1 X e Z e u M e X Z u M Z (1 u M Z u u M 1 1 q 1 g g cos sin u (4 (5 (6 To design a plant model through, we need a longitudinal equation For the dynamics of a longitudinal aircraft, we need variables which are (small deviations from operating point or trim conditions state (components Inputs u : velocity of aircraft along body axis α : angle of attack (the angle between the velocity vector and the x-axis of the aircraft : Angle between body axis and horizontal (up is positive q = : Angular velocity of aircraft (pitch rate ontrol or actuator inputs: e : Elevator angle ( e > is down If we introduce the longitudinal state variable vector x = [u α q ] (1 & the longitudinal control vector u (t = [ e ] ( These equations are equivalent to the system of firstorder equations In x(t = Ax( t Bu( t (3 y( t ( t Du( t x represents the time derivative of the state vector x, and the matrices appearing in this equation are x = I 1 1 n n n A x I B u (7 n On solving (4, (5, (6 and substitute in (7 then we get the approximation form of the linearized equations for longitudinal motions The various dimensional stability derivatives and control derivatives are related to their dimensionless aerodynamic coefficient The selected aircraft Boeing is flying in straight level flight at some altitude with a velocity and the compressibility effects are neglected On the basis of Boeing structures and its aerodynamic configuration, the longitudinal state space model established For this aircraft the values are given below After calculating all the coefficients in matrix A and matrix B, we substitute the values for stability and control coefficient derivatives as shown in table SNo Table 1: Longitudinal Derivatives Aerodynamic Stability Derivatives oefficients Q * S *(* D M * 1 Xu X Q * S *( D L 3 Zu 4 M Q * S * ( * L (1 Mach * L Q * S * ^ * M * Iy * u 5 Z Q * S *( D L 6 Z * Q * S * c * z 7 Q * S * Zq * Lq * 8 Mu Q* S * c * Mach * Iy * u 9 M 1 M q Q* S * c * Iy * u y Q* S * c * * I * u M mq DM ( Mach mm / An open access journal of International Journal Foundation Page I

3 Advance Research Journal of Multi-Disciplinary Discoveries ISSN NO : When the aircraft is in status (H=3g, Mach=35, Velocity=11497m/s, Altitude= 7mThe altitude (Height and velocity will be varying but all the coefficient derivatives will remain constant A Modes of typical aircraft The natural response of most aircraft to longitudinal perturbations typically consists of two under- damped oscillatory modes having rather different time scales One of the modes has a relatively short period and is usually quite heavily damped; this is called the short period mode The other mode has a much longer period and is rather lightly damped; this is called the phugoid mode III DESIGN OF PITH ATTITUDE HOLD MODE There are basically two loops in the design: one inner loop (control loop and one outer loop which controls the top level guidance parameters such as heading or altitude known as (guidance loop The Pitch Attitude Hold mode (PAH controls the pitch angle by applying appropriate deflections of the elevator if the actual pitch angle differs from the desired reference value The pitch angle θ is fed back to damp the phugoid mode and to ensure that the desired pitch angle is maintained A proportional and integrating controller is applied in order to make sure that no steady-state errors in the pitch angle will remain As long as the error signal θ θ ref is not equal to zero, the signal from the integrator will increase, which leads to an increasing elevator deflection which eliminates the error Aircraft Boeing Parameters Altitude-H(metre 7 Flight Mach no(mach 35 True Speed-u(metre/sec Density(Newton/m^ Static pressure(newton/m^ 4161 Dynamic Pressure-Q(Newton/m^ 44 Weight(g 3 Wing area-s(metre^ 5196 Wing chord-c(metre 834 I y (slug/ft^ 33e+6 Pitch angle(θ(degree Longitudinal derivatives D (Drag variations along x axisrad 66 D (Reference Drag coefficient 1 L (Reference lift coefficient 111 DM L (Airplane lift curve sloperad 57 L q (Effect of pitch rate on liftrad 54 L e (Lift force due to elevator deflectionrad 338 mq (Damping in pitchrad -8 m (Static longitudinal stabilityrad -16 m L (Downwash lag on momentrad (Downwash lag on liftrad mm (Effect of slipstream and flexibility and thrust m e (Moment force due to elevator deflectionrad Error! Reference source not found Figure 1: Block diagram of the discrete pitch attitude hold mode Outer loop constitutes a feedback loop of pitch angle It can improve the damping of aircrafts long period motion Parameter selection of control law for the pitch angle control system consists of two parts: the first part is the feedback gain of the damping circuit (inner loop, the second part is the PID parameters in the pitch angle control signal of pitch angle 1 degree Table 1 shows the particular PID values of pitch attitude hold mode for different nine plant models without optimisation which uses trial and error method It is a time consuming method Table 3: Different PID values for different 9 Plant models (Without optimization Plant model Parameters (W=Weight (A=Altitude (M=Mach No W= A=1 M=5 W= A=6 M=45 W= A=1 M=65 W=3 A=1 M=45 W=3 A=6 M=65 W=3 A=1 M=5 W=4 A=1 M=65 W=4 A=6 M=5 W=4 A=1 M=45 Proportional Gain Integral Gain Derivative Gain An open access journal of International Journal Foundation Page I 3

4 Advance Research Journal of Multi-Disciplinary Discoveries ISSN NO : is very less and less overshoot the one we got from the unoptimised controller Figure 5 shows the aircraft closed loop step response for pitch attitude hold mode (with optimisation for-1 degree elevator step input From figure 5 and table shows that after optimisation, the response improves in respect of settling time, and overshoot of a system Figure : Longitudinal Aircraft closed loop step Response for pitch attitude hold mode (without optimization to 1-deg Elevator step Input The figure shows the response for pitch attitude hold mode using PID technique (without optimisation In that graph the settling time and overshoot was more in some plant models To reduce that, we use a technique called PID optimisation It is also known as automatic tuning IV DISRETE PID ONTROLLER (With Optimization For optimisation, we obtain a required response using the second order equation, we choose such a, and ξ value where we get the good step response with minimum overshoot and less settling time ^ s^ ^ Where ɷ= 15 and ξ=9 (8 Now take this as a transfer function, to optimize the PID controller parameters such as p, i, d by using f-min searchthis is chosen so that we get the best response Using these values we obtained a required graph against which all the other plant models will be compared so as we get optimised values of p, i, d It minimises the error between the required and obtained graph to match with the required one Figure 4: Block diagram of pitch attitude hold mode using optimization method V RESULTS P l a n t N o Discrete-ontroller (Before optimisation p i d Set tlin g Ti me (se c Discrete ontroller (After optimisation p i d Settli ng time( sec Table 4: omparison between Discrete and optimized values of PID Error! Reference source not found After optimisation we get the optimised values of p, i, d for all nine plant models The settling time thus obtained Figure 5: Longitudinal Aircraft closed loop step Response for pitch attitude hold mode for 1-deg Elevator step Input (after optimization An open access journal of International Journal Foundation Page I 4

5 Advance Research Journal of Multi-Disciplinary Discoveries ISSN NO : VI DESIGN OF FORWARD SPEED HOLD MODE It is used during cruise flight as a Mach hold mode Aircraft flies at constant Mach through automatic control of pitch angle by the elevator As the aircraft flies the fuel is burned and weight decreases, and speed tends to increase Speed increase detected by control system and corrected by elevator There are basically three loops in the design: two inner loops (control loop and one outer loop which controls the top level guidance parameters such as velocity (guidance loop In the block diagram, the initial speed is given as a unit step input (1m/secThe output is also coming as a step input which indicates the holding of forward speed mode Figure 7 shows the response of forward speed hold mode for unit step input velocity Table 3 shows the gain values for speed hold mode For this mode also we can use optimization technique to get better responses for all the models From the above section, we concluded that optimization have more advantages over without optimization Advantages of PID optimisation 1 The frequency response specifications (settling time, overshoot etc are improved as compared to conventional PID controller It is an automatic tuning method 3 The elevator angle deflection is within the limits (-8 degrees to 8 degrees Trade-offs for PID optimisation 1 The error computation Noise degradation in the derivative control 3 Over simplification and the loss of performance in the control law in the form of linear weighted sum 4 omplications brought by the integral control 5 No active Disturbance Rejection To overcome the trade-offs in PID optimisation, there are various techniques available for plant uncertainty, un-modelled dynamics and disturbance using Active Disturbance Rejection ontrol (ADR scheme that involves an observer design, alman filtering,various estimation techniques etc But still PID controller is more prevalent nowadays because it is the simplest design to develop which caters the problem of dynamics Figure 6: Block diagram of the discrete Forward speed hold mode VII ONLUSION We established the longitudinal equation based on small perturbation and designed the vertical control law of autopilot system of flight simulator using classical control technique More modern control design techniques will be involved in the full six degree of freedom linear autopilot design Make the design of controller based on the states These will be developed using the aircraft plant model Since the model used (Boeing 747 is a general model, and can construct the rnodel of many other aircraft in the same structure Robust autopilot control laws are designed for pitch attitude hold mode and Forwards Speed Hold mode in MATLAB Simulink such as PID (without optimisation, PID (with optimisation More models can be designed for different phases of flight which will define the different set/subsets of experiments with different values of p, i, and d Figure 7: Longitudinal Aircraft closed loop step Response for Forward speed hold mode for 1m/sec -step Input Plant model Proportional controller ( p Integral ontroller ( i Derivative ontroller ( d Table 5: Different PID values for Forward Speed Hold Mode REFERENES [1] Gao jian-shu, Li-Jing, Design and optimisation of autopilot system offlight simulator 1 International conference on optoelectronics and Image processing [] David A Mcaughey Introduction to Aircraft Stability and ontrol ourse Notes for M&AE 57 Sibley School of Mechanical & Aerospace Engineering ornell University Ithaca, New York [3] Princy Randhawa, Vijay Shanthagiri, oncept of Operations to System Design and Development-An Integrated System for Aircraft Mission Feasibility Analysis Using ST Engine, Matlab and Labview 15 International Journal of Instrumentation and ontrol Systems, Volume 5, pp 1-1 An open access journal of International Journal Foundation Page I 5

6 Advance Research Journal of Multi-Disciplinary Discoveries ISSN NO : [4] Mohammad Fiuzy, Javad Haddadnia, Seyed amaleddin Mousavi Mashhadi, Designing an Optimal PID ontroller for ontrol the Plan s Height, Based on ontrol of Autopilot by using Evolutionary Algorithms, Journal of mathematics and computer Science [5] DE Bossert, and ohen PID and Fuzzy Logic Pitch Attitude Hold Systems for a Fighter Jet AIAA Journal of Guidance, Navigation, and ontrol onference and Exhibit, 5-8 August, Monterey, alifornia, ( [6] THS Li, and MY Shieh Design of a GA- based PID ontroller for Non Minimum Phase Systems Journal of Fuzzy Sets and Systems, Vol 111, No, pp , ( [7] V Rajinikanth and Latha Tuning and Retuning of PID ontroller for Unstable Systems Using Evolutionary Algorithm International Scholarly Research Network ISRN hemical Engineering Vol 5, No 3, pp 1-1, (1 [8] B ada, Y Ghazzawi, Robust PID ontroller Design for an UAVFlight ontrol System" Proceedings of the World ongress on Engineering and omputer Science 11 Vol II WES 11, October 19-1, 11, San Francisco, USA [9] amran Turkoglu, Ugur Ozdemir, Melike Nikbay, and Elbrous M Jafarov PID Parameter Optimization of an UAV Longitudinal Flight ontrol System World Academy of Science, Engineering and Technology International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering Vol:, No: 9, 8 [1] G Sudha and S N Deepa, Optimization for PID ontrol Parameters on Pitch ontrol of Aircraft Dynamics Based on Tuning Methods An International of Applied Mathematics and Information Sciences [11] Robert Nelson, Flight Stability and Automatic ontrol, McGraw-Hill, New York, Second Edition 1998 [1] QWang, and R F Stengel, Robust Nonlinear Flight ontrol of a High-Performance Aircraft, IEEE Transactions of ontrol Systems Technology 13, (5 [13] H Ang,G hong and LI Yun, PID ontrol System Analysis, Design, and Technology, IEEE Transactions of ontrol Systems Technology, 13 (5 [14] J Astrom and T Hagllund, PID controllers Theory, Design and Tuning, second edition, Instrument Society of America (1994 [15] Bada and YGhazzawi, Robust PID ontroller Design foran UAV Flight ontrol System, Proceedings of the World ongress on Engineering and omputer Science, (11 [16] SNDeepa, and G Sudha, Longitudinal ontrol of an Aircraft Using Artificial Intelligence, International Journal of Engineering and Technology (IJET 5, (14 [17] SNSivanandam and SNDeepa, ontrol System Engineering using MATLAB, VIAS publishing company Ltd, New Delhi, India (7 An open access journal of International Journal Foundation Page I 6

Artificial Neural Networks based Attitude Controlling of Longitudinal Autopilot for General Aviation Aircraft Nagababu V *1, Imran A 2

Artificial Neural Networks based Attitude Controlling of Longitudinal Autopilot for General Aviation Aircraft Nagababu V *1, Imran A 2 ISSN (Print) : 2320-3765 ISSN (Online): 2278-8875 International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering Vol. 7, Issue 1, January 2018 Artificial Neural Networks