Longitudinal dynamics of a fixed wing aircraft are 4th order (if you include phugoid and short period modes). 

Longitudinal dynamics of a fixed wing aircraft are 4th order (if you include phugoid and short period modes). 

Hello Prof. James

thank you for your answer. how can i find the refrence  that include the Longitudinal dynamics of a fixed wing aircraft ? are you have the that refrence ?

It can be found in numerous textbooks, papers and online resources. 3 textbooks include Stengel; Cook and Stevens & Lewis. A paper that applies SMC to the longitudinal dynamics of an F16 is by  Seshagiri from the 2008 American Control Conference

Prof. James

i downloaded 3 books and 5 paper about your last answer. but i can not find!

if you have the direct link or exact paper about issue. please give that to me. 

Dear James & Javad:

This is the paper link for Seshagiri's work!!

https://www.researchgate.net/publication/224322714_Sliding_mode_control_of_F-16_longitudinal_dynamics

Sliding mode control of F-16 longitudinal dynamics

S. Seshagiri & E. Promtun

Dept. of ECE, San Diego State Univ., San Diego, CA

DOI: 10.1109/ACC.2008.4586748 In proceeding of: American Control Conference, 2008

Source: IEEE Xplore

ABSTRACT We consider the application of a conditional integrator based sliding mode control design for robust regulation of minimum-phase nonlinear systems to the control of the longitudinal flight dynamics of an F-16 aircraft. The design exploits the modal decomposition of the linearized dynamics into its short-period and phugoid approximations. The control design is based on linearization, but is implemented on the nonlinear multiple-input multiple-output longitudinal model of the F-16 aircraft. We consider model following for the angle-of- attack, with the regulation of the aircraft velocity (or the Mach- hold autopilot) as a secondary objective. It is shown through extensive simulations that the inherent robustness of the SMC design provides a convenient way to design controllers without gain scheduling, with transient performance that is far superior to that of a conventional gain-scheduled approach with integral control.

Conference Paper Sliding mode control of F-16 longitudinal dynamics

Hello Prof.Sundarapandian

thank for your suitable answer. i downloaded that paper and read it. but it is not mentioned the four-order dynamical nonlinear equation for F-16 longitudinal dynamics. please download the attach file. i want the equation similar:  x.... +f(x, x.,x..,x...)=c

Equation (1) of Seshagari's paper has the model. It is 5th order because they have included the altitude, but you can apply your SMC controller to the airspeed, angle of attack and attitude only and leave the altitude to an outer loop.Or you can control angle of attack, alpha, rather than pitch attitude, theta, so giving you a 4th order system. 

In ResearchGate, we can at best provide some links, pointers and some general views or beliefs based on our research experience. That's all.

It is too much to expect us to do all the calculations also for the questioners as we are not always the co-authors.

This is a general remark only! Kindly take it in good humour!

With best wishes,

Sundar

Creating an hypothetical but realistic 4th order system should not be too difficult. Just takes two non-linear springs connected together. Or two non linear oscillators connected together. Or just two non linear Hamiltonian systems of second order and define a constraint on the variables. Or just take a two stage switching converter with independent inductor capacitor pairs such that one coverter's output feeds the other.

All these are 4th order non-linear systems. The switching converter is a realistic system. You are most welcome to try sliding mode on it. Let me know your results.

Best wishes

Virendra Sule