Scenario:
You are part of a company that specialises in aircraft control systems and have been tasked with designing an elevator trim system with the following aircraft parameters:
• Elevator trim +/- 30 degrees
• PID control
• velocity feedback damping
• Digital
(i) Design a system to satisfy the parameters given, explain the operation of each component and analyse the system as a whole using appropriate diagrams as required.
(ii) Explain the effects of losing each of the PID functions on the aircraft’s response.
(iii) Compare the characteristics of Coulomb and viscous friction damping; electrical damping and velocity feedback damping and analyse the effects in relation to aircraft control systems.
(iv) Design an alternative system of your choice and explain the overall operation, advantages and disadvantages. Note: your alternate system does not have to follow the parameters.
(i) (a) Always we need to provide elevator trim in aircraft design because the lift forces varies on the wings , straight additive and upright additive vary with the speed of aircraft and the angle of front of the aircraft at which the surrounding air strikes. If the angle of lift of aircraft front edge is +30/ -30 degrees then the drag forces due to air will be minimum and the air thrust experienced will be minimum.
(b) The PID control is provided in aircraft design so that the proportional phrase, integral phrase and derivative phrase gives the required SSE information to the aircraft system, So for proper working of the aircraft system all the three functions of the PID controller are necessary, If the derivative function is not present then the aircraft system can’t work properly but if the proportional or integral function is not present then the derivative function may give the required SSE information to the system.
(c) The velocity feedback damping if speed of the aircraft is high then the velocity sensors may damage and thus will not be able to provide the information regarding velocity of aircraft and it may cause accidents so the velocity feedback damping is always taken into consideration while designing the aircraft.
(d) The role of digital methods in the process of aircraft structure designing is to provide the detailed information to simplify the decisions, the digital are used for these purposes
The design parameters (dimensions) are overall length = 130 ft, cabin length = 95 ft, wheel base = 45 ft, fuselage width = 15 ft, maximum cabin width = 13 ft, wing span= 120 ft with shark lets, height = 40 ft, track = 25 ft,
(ii) The PID functions in a aircraft can be defined as proportional integral derivative and can be expressed as v = Cpe + CID
Here Cp, CI and CD are the controller parameters which we have to elect. There is combination of three functions in PID controller and operates on the error in the feedback system and performs the following operations
A PID controller evolutes the error comparative to the P phrase A PID controller evolutes the error comparative to the I phrase A PID controller evolutes the error comparative to the D phrase The above three phrases are added together to give a control signal to the system which have to be controlled.
With the help of PID controller we can judge the manner of system and controller
If we lose a proportional function of a PID controller then it will not be able to give the SSE routine needed in the aircraft system.if we lose a integral function of a PID controller then it may produce the SSE routine needed, but it will time-consuming the aircraft system.If we lose a derivative function of a PID controller then the PID will not be able to produce any of the above functions but we add derivative phrase then the PID may be able to produce the information needed by the above proportional and integral phrase.
In the three boxes the upper box is of proportional phrase, middle is of integral phrase ,lower is of derivative phrase.
The PID controller makes a pole at the origin , according to the designers choice it can be designed as
PID (s) = [sCP +CI +s2CD] / s.
(iii) The coulomb damping can be defined as a mode of energy loss due to sliding motion which comes in consideration due to friction, as there is always friction acts between two mechanical components and causes a certain loss of energy from its kinetic energy and dissipate the same in the form of heat so if the heat generation is more it will affect the control system of aircraft and after a certain level of coulomb damping the control system will not be in proper working. Whereas viscous damping is the result of viscous force acting on aircraft due to the viscosity of air, it also dissipates the kinetic energy of aircraft and will be high if the velocity of aircraft is high. The coulomb damping presents in internal parts of aircraft whereas viscous damping acts on exterior parts of the aircraft.
The electrical damping can be explained as the loss of electrical energy due to rise of temperature because of resistance, this energy loss is in the form of heat. So after a certain limit the heat generated due to the electrical damping it will affect the control system of aircraft and the high heat may damage the electrical and mechanical components of aircraft like sensors. The velocity feedback damping can be defined as somewhat by the side of the lines of an supplementary control unit has speed sensor involved thus in turn feeds the supplementary power control unit which uses the suggestion to manage the speed of the aircraft control unit. So if the velocity feedback damping is more than the speed sensors will not be in proper working and the controller of the aircraft will not be able to judge the speed of aircraft and it may cause accidents.
(iv). A system can be designed with two controllers , linearised steering model and feed forward design , PID control with the following data wing span = 42 m, height = 11 m, length = 35 m,
wing area = 160 m2, elevator trim = +160 / -160 ,viscous damping , velocity feedback damping, air thrust ,maximum height attenable
Feed forward design has feed forward compensator to be stable and that is not require differentiation.
The linearised steering replica can be controlled by normalize transfer function commencing steering angle 0 to sideways variation is P(s) = (1 +0s) / s2. The biggest steering point of view is somewhat larger than 0.12 rad (50). The preferred comeback of steering F(s) = c2 / (s2 + c2) where the act in response rate or assertiveness of the steering is governed by the parameter c. Fv = Fn /P
Fv = c2s2 / (1 +0s)(s+c)2
Which is stable transfer function as long as 0 > 0.
The major advantage of two controllers having two degree of freedom that combine feedback and feed forward motion is that the control design problem can be split in two parts the feedback controller can be designed to give good robustness and effective disturbance attenuation and forward can be designed independently to give the desired response to the command signals. Also the will drive four blade constant speed propellers.
The only disadvantage of designing such a system is that the system will be heavier and can only assist in making it a fighter craft, it will not be suitable for commercial purpose as its speed will be high as 630 km/hr and its max. Take off capacity will be around 75 tons. So it will be more efficient if we make it either a fighter or low sitting capacity aircraft.
References-
1. P.-A. Bliman. Mathematical study of the Dahl’s friction model. European Journal of Mechanics. A/Solids, 11H6I:835–848, 1992.
2. B. Armstrong-Hélouvry, P. Dupont, and C. Canudas de Wit. A survey of models, analysis tools and compensation methods for the control of machineswith friction. Automatica, 30H7I:1083–1138, 1994.
3. Franklin, G. F., J. D. Powell, and A. Emami-Naeimi, “Feedback Control of Dynamic Systems,” 3rd ed., Addison-Wesley,1994.
4. Goodwin, G. C., S. F. Graebe, and M. E. Salgado, “Control System Design,” Prentice Hall, 2001.
5. Gao, Z., Y. Huang, and J. Han, “An Alternative Paradigm for Control System Design,” Presented at the 40th IEEE Conference on Decision and Control, Dec 4–7, 2001, Orlando, FL.
6. Kuo, B. C., “Automatic Control Systems,” 7th ed., Prentice Hall, 1995.
7. Ogata, K., “Modern Control Engineering,” 3rd ed., Prentice Hall, 1997.
8. Rohrs, C. E., J. L. Melsa, and D. G. Schultz, “Linear Control Systems,” McGraw-Hill, 1993.
9. Trimmed Aircraft. 2015. Trimmed Aircraft. [ONLINE] Available at:https://www.grc.nasa.gov/WWW/K-12/airplane/trim.html. [Accessed 12 March 2015].
10. Aircraft Designs. 2015. Aircraft Designs. [ONLINE] Available at: https://www.aircraftdesigns.com/. [Accessed 13 March 2015].
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