In fact, you want to talk about equilibrium points, the Russians have advanced in this field so much that they've been using TVC on many of their jets (SU-30 MKI an example sold to India). Where the thrust vector actually requires much advanced equilibrium control computations to take place by SU-30's flight computers, additionally, both Relax and Static surfaces are used (hybrid model) to maneuver around the shift in velocity, balance, drag and equilibrium dislocation (due to sudden aerodynamic, gravitational and wind related forces acting in within a mil-second as the TVC's are applied).
@Viper0011.
You sure what you said is correct?I would like you to take a look again?Do you really think by having a different dimension of control vector U,one can have a different system matrix A?The answer is No! The system matrix A and it's dimension depend on the variables in a system we assume to be "state variables"- it is NOT unique as it depends on the choice of the state variables.- as a SIMILARITY TRANSFORMATION would prove(I am sure you would know similarity transformation?).
But once we have decided the state variables for instance v,alpha,beta,theta etc then what it means is,we have fixed the system matrix A. And once we have fixed system matrix A- it means we have fixed the "static" and "dynamic" properties of a fighter jet. Pardon me if i am going a bit technical ,but i see no other way to make you understand that characteristics of system matrix is INDEPENDENT Of choice of control vector U.
I am sure you'd agree that nullspace of (s*I-A) is nothing but the eigenvector(lets denote it by vector V) of our system matrix.--------------
eqn 1
A fighter jet is said to be dynamically unstable if the real part of all the eigenvalues of system matrix A lies on the right half plane(this is INDEPENDENT of choice of control vector U). What we mean by "dynamic" is by observing the flight of the plane over a period of time and if it breaks into ever-increasing oscillations over large period of time then it is said to be "dynamically unstable"."Static" on the other hand refers to short period dynamics- a jet is said to be "statically unstable" if it has tendency to recede away from equilibrium point(for instance ever-increasing pitch attitude) right after it has been disturbed from itz equilibrium point(trim state).Static unstability results from the fact that your CG is aft of neutral stick fixed point.ANd neutral stick fixed point is obtained by equating the C em alpha =0,I.e dC/dalpha=0 or variation of pitching moment wrt alpha equals 0.
You see,what i am trying to say is the inherent property of a fighter jet i.e its static or dynamic stability/instability is determined by position of CG and the system matrix A respectively and not by the choice of control input U(TVC in your case).Where TVC matters is the design of control law as i will explain below-
Now i will touch upon the part where control vector U really matters and that is - in designing CONTROL LAW. Well unlike other applications of control systems engineering wherein simple PID,feedback,feedforward control strategies normally yield desirable results and where the system is not expected to have more than one equilibrium point
**, Aerospace controls requires extensive use of control system design in state space. WHat we essentially do here is,find the gain vector K that will yield the desired aircraft performance(considering control vector U).One can approach this problem in many ways- some of the ways are-
1)Ackerman formulation
2)Optimal control
3)Eigen-structure Assignment problem.
#2 is the preferred choice in missiles and #3 in aircrafts
PS-
a)
eqn-1 is used in #3 to determine the gain matrix K=UV^(-1) or K= U times V inverse
b)
** stability is a function of equilibrium point and in traditional systems like thermal power plants etc ,there exists only one equilibrium point for all the state variables.However in aerospace there exists a lot of equilibrium points and the system matrix A changes accordingly because we are linearizing our 8 NON-LINEAR AND COUPLED DIFFERENTIAL EQNs around each equilibrium point.
c)I use python to code everything i have written above however if you wish to implement it on a piece of hardware then you would need either C++ or ADA- preferrably ADA because it is becoming norm in aerospace thanks to boeing
RSS in terms of Relax Static Stability is in the JFT already. If you see a most recent aerobatics display by the JFT, you can very quickly see the -16's like RSS capability during flight and almost immediate smooth relaxed flight characteristics from quick G-turns, nose dives (nose pointing), directional differentiation and other performance points.
I didnt know that one can determine if a plane has RSS simply by looking at the performance of the jet in airshows. However,in real academic terms you need to furnish literature or prove it using equations/engineering/logic etc
For example I can get 10 guys sharp with C++ for the likes of Cognizant, Satyams, Delloittes of the world for like $ 25 an hour from India. That's where future of these jets will be going.
Sure you can get them cheap,but will they have background in aerospace engineering?I doubt that pretty much.Besides i have not seen in my experience anyone from these companies writing control laws for fighter jets. yeah,but i agree,anyone can code a control law in either C,ADA or python provided he knows what a control law is- it is like knowing algorithm