Mark Costello

Aspects of Control for a Parafoil and Payload System

A parafoil controlled by parafoil brake dee ection offers a lightweight and space-efe cient control mechanism for autonomous placement of air-dropped payloads to specie ed ground coordinates. The work reported here investigates control issues for a parafoil and payload system with left and right parafoil brakes used as the control mechanism.Itisshownthatparafoilandpayloadsystemscanexhibittwobasicmodesoflateralcontrol,namely,roll and skidsteering.Thesetwo modesoflateralsteeringgeneratelateralresponseinoppositedirections.Forexample, a roll steer cone guration turns left when the right parafoil brake is activated, whereas a skid steer cone guration turnsright under the samecontrol input. In transition between roll and skid lateral steering, the lateral responseis zero, and the system becomes uncontrollable. Angle of incidence, canopy curvature of the parafoil, and magnitude of brake dee ections are important design parameters for a controllable parafoil and payload system and greatly effect control response, including whether the basic lateral control mode is roll or skid steering. It is shown how the steering mode switches when fundamental design parameters are altered and as the magnitude of the brake dee ection increases. The mode of directional control transitions toward roll steering as the canopy curvature decreases or the angle of incidence becomes more negative. The mode of directional control transitions away from the roll steering mode as the magnitude of the brake dee ection increases, and for “ large” brake dee ections most parafoils will always skid steer.

Model Predictive Control Of A Parafoil And Payload System

A model predictive control strategy is developed for an autonomous parafoil and payload system. Since the technique requires a linear dynamic model of the system, a reduced state linear model based on a nonlinear 6 degree-of-freedom parafoil and payload model is established and validated. In order to use the reduced state linear model for model predictive control the desired trajectory in the x-y plane is mapped into a desired heading angle using Lagrange interpolating polynomials. Flight test results demonstrate that this model predictive control strategy is a natural and effective method of achieving trajectory tracking in a parafoil and payload system.

Nonlinear Model Predictive Control Technique for Unmanned Air Vehicles

A nonlinear model predictive control strategy is developed and subsequently specialized to autonomous aircraft that can be adequately modeled with a rigid 6-degrees-of-freedom representation. Whereas the general air vehicle dynamic equations are nonlinear and nonaffine in control, a closed-form solution for the optimal control input is enabledby expandingboth the output and control in a truncatedTaylor series. The closed-form solution for control is relatively simple to calculate and well suited to the real time embedded computing environment. An interesting feature of this control law is that the number of Taylor series expansion terms can be used to indirectly penalize control action. Also, ill conditioning in the optimal control gain equation limits practical selection of the number of Taylor series expansion terms. These claims are substantiated through simulation by application of the method to a parafoil and payload aircraft as well as a glider.

Use of Variable Incidence Angle for Glide Slope Control of Autonomous Parafoils

Strictly speaking, most autonomous parafoil and payload systems possess only lateral control, achieved by right and left parafoil brake deflection. An innovative technique to achieve direct longitudinal control through incidence angle changes is reported. Addition of this extra control channel requires simple rigging changes and an additional servoactuator. The ability of incidence angle to alter the glide slope of a parafoil and payload aircraft is demonstrated through a flight-test program with a microparafoil system. Results from the flight-test program are synthesized and integrated into a six degree-of-freedom simulation. The simulation model is subsequently used to assess the utility of glide slope control to improve autonomous flight control system performance. Through Monte Carlo simulation, impact point statistics with and without glide slope control indicate that dramatic improvements in impact point statistics are possible using direct glide slope control.

Linear Theory of a Dual-Spin Projectile in Atmospheric Flight

Abstract : The equations of motion for a dual-spin projectile in atmospheric flight are developed and subsequently utilized to solve for angle of attack and swerving dynamics. A combination hydrodynamic and roller bearing couples forward and aft body roll motions. Using a modified projectile linear theory developed for this configuration, it is shown that the dynamic stability factor, S(g), and the gyroscopic stability factor, S(g) are altered compared to a similar rigid projectile, due to new epicyclic fast and slow arm equations. Swerving dynamics including aerodynamic jump are studied using the linear theory.

Model predictive lateral pulse jet control of an atmospheric rocket

Uncontrolled direct fire atmospheric rockets exhibit high impact point dispersion, even at relatively short range, and, as such, have been employed as area weapons on the battlefield. To reduce the dispersion of a direct fire rocket, the use of a small number of short-duration lateral pulses acting as a control mechanism is investigated. A unique control law is reported that combines model predictive control and linear projectile theory for lateral pulse jet control of an atmospheric rocket. The impact point in the target plane is directly controlled. Through simulation, this model predictive flight control law is shown to efficiently reduce direct fire rocket dispersion. A parametric trade study on an example rocket configuration is reported that details the effect of the number and amplitude of individual pulse jets, as well as the effect of the flight control system computation cycle time.

Modified Projectile Linear Theory for Rapid Trajectory Prediction

In some smart weapons, estimation of the impact point of the shell at each computation cycle of the control law is an integral part of the control strategy. In these situations, the impact point predictor is part of the imbedded computing system onboard the projectile. Practical considerations dictate that the impact point predictor yield rapid yet reasonably accurate estimates. Common methods for rapid trajectory prediction are numerical integration of point mass dynamic equations and evaluation of approximate closed-form solutions of the rigid-body projectile dynamic equations. These methods are shown to exhibit poor impact point prediction for long-range shots with high gun elevations characteristic of smart indirect fire munitions. Through modifications of projectile linear theory, a rapid projectile impact point predictor is proposed that eliminates the accuracy problems of the other methods while preserving low computational requirements. Typical results are provided for a short-range trajectory of a direct fire fin-stabilized projectile and a long-range trajectory for an indirect fire spin-stabilized round to substantiate these claims.

Dispersion Reduction of a Direct Fire Rocket Using Lateral Pulse Jets

Impact point dispersion of a direct e re rocket can be drastically reduced with a ring of appropriately sized lateral pulse jets coupled to a trajectory tracking e ight control system. The system is shown to work well against uncertainty in the form of initial off-axis angular velocity perturbations as well as atmospheric winds. For an example case examined, dispersion was reduced by a factor of 100. Dispersion reduction is a strong function of the number of individual pulse jets, the pulse jet impulse, and the trajectory tracking window size. Proper selection of these parameters for a particular rocket and launcher combination is required to achieve optimum dispersion reduction. Forrelatively lowpulsejetimpulse, dispersion steadily decreasesasthenumberofpulsejetsisincreased or as the pulse jet impulse is increased. For a e xed total pulse jet ring impulse, a single pulse is the optimum pulse jet cone guration when the pulse jet ring impulse is small because the effect of a pulse on the trajectory of a rocket decreases as the round e ies downrange. Nomenclature CDD = e n cant roll moment aerodynamic coefe cient CLP = roll damping aerodynamic coefe cient CMQ = pitch damping aerodynamic coefe cient CNA = normal force aerodynamic coefe cient CX0 = zero yaw axial force aerodynamic coefe cient CX2 = yaw axial force aerodynamic coefe cient D = rocket reference diameter ethres = trajectory tracking window size L; M; N = total applied moments about rocket mass center expressed in the aft body reference frame nJ = number of individual lateral pulse jets nRXi ;nRYi , = ith main rocket motor direction cosines in the nRZi body frame p;q;r = components of the angular velocity vector of the projectile in the body reference frame T = P ° time constant TJi = ith lateral pulse jet thrust TRi = ith main rocket motor thrust t ¤ = time of the most recent pulse jet e ring u;v;w = components of the velocity vector of the mass center of the composite body in the body reference frame uA;vA;wA = components of the velocity of the mass center of the projectile with mean wind expressed in the body reference frame VA = magnitude of the velocity vector of the mass center of the projectile experienced with mean wind expressed in the body reference frame VMW;aeMW = magnitude and wind factor of the mean atmospheric wind expressed in the initial reference frame X;Y; Z = total applied force components in the aft body reference frame

Prediction of swerving motion of a dual-spin projectile with lateral pulse jets in atmospheric flight

Using the linear theory for a dual-spin projectile in atmospheric flight, closed form expressions are obtained for swerving motion under the action of lateral pulse jets. Trajectory results generated by the linear theory equations and a fully nonlinear seven degree-of-freedom dual spin projectile model agree favorably. The analytic solution provides a relatively straightforward and computationally efficient means of trajectory estimation which is useful within smart weapon flight control systems. In order to accurately predict the impact point using the analytic solution, the dual-spin projectile linear model must be updated periodically. Terminal impact point prediction degrades rapidly as the linear model update interval is increased beyond a critical value. Control authority, as defined by the change in impact location due to a pulse jet firing, steadily decreases as a function of projectile down range position.

Control Authority of a Projectile Equipped with a Controllable Internal Translating Mass

control authority requirements. The work reported here considers a vibrating internal mass control mechanism applicableto both fin-and spin-stabilized configurations.To investigate the potential of this control mechanism, a7degree-of-freedom flight dynamic model of a projectile equipped with an internal translating mass is generated. By vibrating the internal translating mass normal to the axis of symmetry and at the roll rate frequency, significant control authority can be attained with a relatively small internal mass on the order of a percent or so of the total projectile mass. Interestingly, control authority increases proportionally with increasing roll rate and also with increasing station-line cavity offset from the mass center. Trajectory changes are not caused by lateral mass center offset and drag but rather by dynamic coupling between internal mass vibration and the projectile body. Nomenclature AT = internal translating mass oscillation amplitude aC=I = translational acceleration vector of the system center of mass with respect to the inertial frame aP=I = translational acceleration of the projectile center of mass with respect to the inertial frame aT=I = translational acceleration vector of the internal translating mass center of mass with respect to the inertial frame aT=P = translational acceleration of the internal translating mass with respect to the projectile reference frame B = point at center of internal translating mass cavity