DAMPING OF OSCILLATIONS IN FLIGHT CONTROL CIRCUITS OF SCHOOL AND TRAINING AIRCRAFT

Transcription

1 DAMPING OF OSCILLATIONS IN FLIGHT CONTROL CIRCUITS OF SCHOOL AND TRAINING AIRCRAFT Bogdan DOBRESCU, INCAS, Radu BOGĂŢEANU, INCAS, Ion NILĂ, INCAS, DOI: / Abstract The specific developments of Dutch roll mode have shown a number of flight dynamics deficiencies, prevailing in aircraft with fixed (non-assisted) controls in which the damping factor is at level 2. The project deals with the lateral motion damping (damper of gyration) issue according to the flight regulations, for an envelope as wide as possible, but mainly referring to missions involving the Dutch roll type developments. The undertaken analysis takes as a reference the school and training aircraft IAR 99. The execution equipment, an actuator assisted by a servo valve, ensures the system efficiency of self-stabilization system SAS providing low execution times and high precision. The relationship between the flight quality parameters related to characteristics of lateral-directional motion modes, depending on gravimetric-inertial and aerodynamic parameters of the airplane is envisaged to meet the regular levels of flying qualities. The proposed calculation method can be used both for flight qualitative analysis and for defining the overall conditions for meeting the quality flight regulations. These conditions can serve as a basis for assessing the possibilities to remedy the abovementioned deficiencies mater. Introduction School and training aircraft are usually equipped with conventional control systems, nonassisted mechanical systems. These planes have a low damping factor at speeds above Mach 0.3 and altitudes of over 5000 m. The proposed analysis is based on research made on military school and training aircraft IAR 99. With this category of aircraft an unsatisfactory level of damping oscillations was found, especially in the missions requiring Dutch roll mode specific developments. According to calculations of stability, the damping factor of the Dutch roll mode is of level 2 in almost all the operational envelope. The oscillations damping can be achieved by adding an automated system to the direction controls in order to reduce them to the level required by regulations. In this case the system will function as a gyration damper with reaction depending on the speed of gyration (r r). The Dutch roll specific natural frequency for the category of the analyzed aircraft is of level 1 for all configurations and in the entire flight envelope. According to the pilots observations made during the flight tests, as well as to the analysis of the specialists in flight dynamics it follows that the evolutions in Dutch roll mode of the school and training aircraft are deficient in terms of oscillations damping at level 1. The study on the active increase of the Dutch roll damping factor by using a damper of gyration, shall comply to the following: global requirements to meet regular levels of quality flight [1]. Equations of the lateral-directional perturbed motion Dimensional equation of lateral-directional motion, obtained by general motion equations in the case linarizarea small perturbation around solutions for the representation of symmetric stationary flight [2] are: 12

2 (1) Expressing from the first equation of system (1) and solving the equations system consisting of the second and third equation in relation to the r and p unknowns, equations (1) get the usual canonical form of a linear dynamic system: (2) 13

3 To study the stability with fixed controls the following equations are considered: (3) Solutions calculation of this equations system starts from the characteristic polynomial: (4) Typically the matrix A has as eigenvalues the roots of the polynomial as follows: - a pair of complex conjugate eigenvalues: Two real eigenvalues and, with time constants (5) (6) To obtain a particular transfer functions Cramer's rule can be applied. This transfer function, such as the aileron and roll angular velocity will be expressed in terms of characteristic polynomial and can be written as: (7) Parameters assessing the flight qualities with respect to dynamic stability with fixed controls [3], [4] refer mainly to the characteristics of flight modes: the damping factor, natural frequency, number of cycles of half-life, doubling time, half-life, etc. The qualitative analysis of flight require the calculation of eigenvalues of matrix A (2), which does not cause problems if the matrix A is indicated numerically. In this case analytical expressions of eigenvalues of matrix A are considered. For this purpose the analytical solution of the equation of degree 4 P( ) det( I A) 0 is very difficult to solve and doesn't highlight the periodic or a periodic nature of the modes. Because of this simplified models of the lateral-directional motion, with fewer degrees of freedom, which approximate only a mode or at most two modes, are needed. The adoption of such models (i.e. the choice of degrees of freedom [5]) will be made depending on the weight of the modes to be approximated occur in the,r, p, variables variation. 14

4 The calculation model of roll and spiral modes, with three degrees of freedom To obtain a simplified model of motion which characterize only the roll and spiral modes the following assumptions are considered: - In variations the roll mode is poorly represented while the spiral mode is almost nonexistent - the ' Y quantity related to the spiral mode is negligible compared to the amount of other component of lateral force. Considering the above observations, the first of equations (3) is transformed into an algebraic equation, so that to be obtain the following simplified model (YP = 0), with three degrees of freedom: From equation (8) expression r is obtained: INCAS BULLETIN, Volume 2, Number 1/ 2010 (8) (9) (10) (11) (12) Replacing this expression in (9), (10) and (11) it results differential equations depending on, p and : (13) (14) (15) Extracting p from (15) and replacing it in (13) and (14) and replacing from the remaining system, respectively, lead to the differential quadratic equation: (16) where: (17) 15

5 (18) The characteristic polynomial of these differential equations is: (19) And roots of the polynomial are: (20) (21) These expressions of roots approximate well enough the specific values of the Dutch roll and spiral modes. Maximum permissible delay control system The automatic system of stability increase by intervening in the directional and aileron control circuit was approached at a simplified level, purely in terms of flight dynamics and not of automated systems dynamics. In this case the system equations can be written as follows: (22) Where u (t) is the command and has the form: Command u (t) will be "quick" when reading state x, without any delays specific to the airplane subsystems, whose inertia is manifested differently. K synthesizes the behavior of stability increase automatic system, without regard to the fact that each subsystem separately has its own frequency response. To states x the state of Washout filter and the element execution status can be added. In this case the control law is written as: If a delay of states to be corrected with the amplification factor is considered the control expression becomes: (25) (23) (24) 16

6 By applying Laplace transform to the resulting system after the replacement of u (t) the characteristic equation is finally obtained in the variable s, written as matrix (the characteristic determinant): Where B r is the first column of matrix B and I is the unit matrix. To estimate the required accuracy, simulations of the response in time of the states and signal collected from the feedback loop, without pilot control are made at various initial values of the disturbed state r. For the measurement errors to be considered disturbances the precision of the measurement instrument must be at least an order of magnitude higher compared to the measurements. Therefore, we can consider the measurement domain of the instrument through the relation: Where the coefficient c m can be situated from 1.5 to 2. The algorithm utilized to establish the maximum delay when s) ( ) : ( D min INCAS BULLETIN, Volume 2, Number 1/ 2010 ( r ) on the feedback loop is: The damping factor (s) (where s is a complex number) is determined at each iteration. When ( s) ( D) min, r ( r ) max is deduced from the step number n, which is the maximum permitted value of the delay at the feedback loop. max (26) (27) (28) (29) (30) The main requirements imposed to the self-regulation system The self -regulation system shall meet the following main requirements in terms of functional and structural features: To ensure the lateral movement damping (gyration damper) at the level imposed by regulation (MIL-F-8785C), for a flight envelope as wide as possible, but mainly referring to specific missions involving the Dutch roll type evolutions; To react quickly enough to the dynamic disturbances and ensure an optimal stability; Stabilization to be done fast enough, with reaction times as low as possible; To fit in with the aircraft structure without affecting its other systems from the structural and operational point of view. Operational diagram of a self-stabilization system, SAS Fig. 1 shows the block diagram of the self-stabilizing system that is characterized, according to the diagram, by the reaction r r, from the speed of response to the deflection of direction. 17

7 Fig. 1 - The block diagram of the self-stabilizing system According to the diagram one can notice that the amplification factor Kr, is influenced by the Washout filter that provides the transfer function. This filter has the function "move up" meaning that it disengages the reaction in steady regime (at low frequencies) and eliminates the reaction opposition in turn flight, which allows the damping for small deflections in direction or ailerons control. The limiter has the function of a saturation amplifier with unitary amplification factor for which the saturation threshold sets the authority level of the closed-loop control (feedback). The direction damping is based on the determination of the amplification factor, Kr and of time constant, τ of the Washout filter, so that the damping factor of the Dutch roll mode of the system in closed circuit, aircraft + damper of gyration, to be of level 1 across the entire flight envelope, for the chosen computation configuration, according to MIL-F-8785C regulation[6]. The disturbance of the gyration speed, r, reported to a reference value is detected by the gyrometer. It delivers electrical signals (er) to the computational system which will send an output control signal (e ' r), signal to be filtered by the Washout filter resulting in a control signal (s r),directly applied to the drive system, which will occur through the operating rod in the control circuit to eliminate or mitigate the disturbance. The perturbation is given by the variation of condition (speed of gyration r) affecting the modal parameter required by the flight qualities regulation, parameter that should be of level 1. The reaction (r r) depends on the time constant τ, so that the damping factor increases with the decreasing value of the filter time constant. The performed analyses and researches have as reference the training and school military aircraft IAR These aircraft, within their training special missions, requiring specific developments in the Dutch roll mode, have a low level of oscillations damping. The damping factor of the Dutch roll mode according to the performed stability calculations is of level 2 in almost all the operational envelope. The oscillations damping is performed by introducing a self-stabilizing system into the direction control operating as a reaction damper of gyration depending on the rate of gyration (r r). The efficiency of the self-stabilizing system, SAS, is determined by the execution equipment Fig. 2, which must have low reaction time and high accuracy. 18

8 Fig. 2 Servoactuator Main blocks of the SAS system Rotary transducer for converting the rotation displacement into analog electrical signal Rudder bar Kinematics linkage of the direction control Load simulator for providing neutral position Rotary transducer for converting the rotation displacement into analog electrical signal Washout Filter Gyrometer to measure the angular velocities of the airplane towards the trihedral originated in the center of mass The computational system with suitable interface for processing signals from instrumentation. The interface also ensures the signal amplification and filtering. The airplane dynamics: occurs by the laws of linearization of lateral-directional motion of the plane The Block Data: includes instrumentation and subsystems for calculating height, speed, temperature and incidence of flight. The servoactuator parallel to the kinematics linkage of the direction control o The control law implemented in the computational system also depends on the amplification factor Kr; the amplification varies with the height and speed of flight. o The actuator and the rotary transducer can form a closed-loop drive subsystem, which allows very rapid corrections of the actuator rod displacement and finally deflection corrections which are needed to a proper run of direction. 19

9 Conclusions The present study and calculation highlight the flight dynamics deficiencies, mainly for the Dutch roll mode in airplanes with fixed controls. The dimensional equations of the lateraldirectional motion are determined and the parameters which assess the flight qualities in terms of dynamic stability are highlighted. The study presents a simplified calculation, model suitable for the lateral-directional motion with three degrees of freedom. The simplified model, which refers to no more than two flight modes allows the analysis and established the periodic or periodic modes of flight. The analysis of results for regular quality parameters of flight in the two cases, namely the simplified model with three degrees of freedom and complete linearized model, found that the values obtained are very close, these calculations were made for 12 specific flight conditions for subsonic aircraft. The approximation of the modes of motion allows the expression of modal parameters depending on aerodynamic derivatives and inertial parameters that influence the damping factor of the Dutch roll oscillations, so that it is 1. These conditions allow analyzing the possibilities of remedying the deficiencies of stability using permitted means of constructive nature, by implementing a gyration damper system reacting depending on the gyration speed (r r). REFERENCES [1]. Military Specification: Flying Qualities of Piloted Airplanes, MIL-F-8785C [2]. STEVENS B. and LEWIS F., Aircraft Control and Simulation, John Wiley and Sons, 2003 [3]. Stabilitatea dinamica laterala si de directie cu comenzi libere si blocate, raport INCREST, cod AS-212, 1981 [4]. Raport final privind stabilitatea avionului IAR-99, INCREST, 1982 [5]. BERNARD ETKIN, Dynamics of Flight-Stability and Control, John Wiley and Sons, 1959 [6]. Studiu dinamic si evaluarea parametrilor de lucru pentru sistemul de autostabilizare SAS, INCAS,