Nathan Harl

Impact Time and Angle Guidance With Sliding Mode Control

A novel sliding mode-based impact time and angle guidance law for engaging a modern warfare ship is presented in this paper. In order to satisfy the impact time and angle constraints, a line-of-sight rate shaping process is introduced. This shaping process results in a tuning parameter that can be used to create a line-of-sight rate profile to satisfy the final time and heading angle requirements and to yield acceptable normal acceleration values. In order to track the desired line-of-sight rate profile in the presence of uncertainties, a novel robust second-order sliding mode control law is developed using a backstepping concept. Due to the robustness of the control law, it can be applied to many realistic engagement scenarios which include uncertainties such as target motion. Numerical simulations with different warship engagements are presented to illustrate the potential of the developed method.

Reentry Terminal Guidance Through Sliding Mode Control

A guidance scheme has been developed for the terminal guidance of an unpowered lifting reentry vehicle during the approach and landing phase. The proposed approach is quite useful for offline trajectory design and allows for trajectories to be generated online through the use of a closed-loop control law. In scenarios in which the reentry vehicle is significantly deviated from its nominal trajectory upon entry into the landing phase, the usefulness of such an online method can be clearly realized. These types of scenarios are of interest for any reentry vehicle, including the space shuttle, since existing guidance approaches during the approach and landing phase involve tracking trajectories created offline. To solve the approach and landing guidance problem, a novel concept called the sliding mode terminal guidance is used in this work. This approach takes advantage of the finite-time-reaching phase of the sliding mode technique to ensure that any desired state constraints can be fulfilled in a finite time. Further, by using a new approach to second-order sliding mode control, analytic solutions are obtained for both the altitude and flight-path angle during the reentry process. The end result of this approach is a closed-loop guidance (control) law, which can be used to generate trajectories that depend only on the initial and final conditions of the approach and landing phase. Simulations shown indicate that the method provides some robustness to variations in the initial downrange and velocity.

Sliding Mode Integrated Missile Guidance and Control

A novel method for the integrated guidance and control of a missile, called Sliding Mode Integrated Guidance and Control (SMIGC), is derived. In this formulation, the guidance and control systems are developed together and implemented in a single loop. One benefit of this “integrated” approach is that beneficial synergies between the guidance and control subsystems can be exploited. The design process can also be significantly reduced since only one control architecture must be designed. SMIGC makes use of the finite(time reaching phase of the sliding mode technique to ensure that a desired constraint, the Predicted Impact Point (PIP) heading error, is achieved in a finite time. Furthermore, the robustness of sliding mode to uncertainties is combined with a novel method for accounting for target acceleration to yield acceptable miss distances against maneuvering targets. An interesting and desirable aspect of the controller is that it does not require full information about the target acceleration. Further, to fully understand the effects of target acceleration on the problem, an in(depth target acceleration uncertainty analysis is performed. The effectiveness of the SMIGC approach is demonstrated through a series of simulations with a 6(DOF nonlinear missile model that includes all aerodynamic effects against maneuvering targets. Representative numerical results show that against agile targets, SMIGC obtains a high Hit(to(Kill accuracy consistently with reasonable fin deflections. �omenclature

Co-Ordinated Rendezvous of Unmanned Air Vehicles to a Formation Using a Sliding Mode Approach

A method for the co-ordinated rendezvous of a team of unmanned air vehicles (UAVs) to a formation through the use of sliding mode control is presented. The focus of this work is on the scenario where three ‘follower’ UAVs must rendezvous in a desired formation about a ‘Leader’ UAV in a finite time. An assumption is made that each UAV only receives knowledge of the bounds of the manoeuvres that the other UAVs are performing. By not requiring manoeuvre information to be constantly available, a level of robustness to possible communication outages between UAVs is obtained. The proposed method also guarantees that the formation will be achieved in a finite time through the use of a concept of sliding mode terminal guidance (SMTG). SMTG takes advantage of the finite-time reaching phase of sliding mode to ensure that any desired constraint can be fulfilled in a finite time.

Neural Network Based Modified State Observer for Orbit Uncertainty Estimation

A novel technique for estimating uncertainties caused by gravitational perturbations is presented. The approach, called the modified state observer, allows for the estimation of uncertainties in nonlinear dynamics and, in addition, providing estimates of the system states. The observer structure contains neural networks whose outputs are the uncertainties in the system. A useful and important application of this observer is the problem of determining uncertain gravitational perturbations that a satellite may experience when orbiting a body. With future space missions involving other bodies, such as asteroids that produce gravitational perturbations which are highly uncertain and are subjected to unknown physical influences, the modified state observer can be used not only to estimate the states of the satellites, but it can also be used to estimate the uncertainties that could be analyzed further with understanding the physical phenomena. To demonstrate the utility of the modified state observer for this ...

Modified State Observer for Orbit Uncertainty Estimation

A novel technique for estimating uncertainties caused by gravitational perturbations is presented. The approach, called the Modified State Observer (MSO), allows for the estimation of uncertainties in nonlinear dynamics while in addition providing estimates of the system states. The observer structure contains neural networks whose outputs are the uncertainties in the system. A useful and important application of this observer is the problem of determining uncertainties with an inaccurate gravity mode that a satellite may experience when orbiting a body. With future space missions involving other bodies such as asteroids that produce gravitational perturbations which are highly uncertain and are subjected to unknown physical influences, the MSO can be used not only to estimate the states of the satellites, it can be used to estimate the uncertainties that could further be analyzed further in understanding the physical phenomena. To demonstrate the utility of the MSO for this class of problem, the technique is applied for three cases: estimating the uncertainty caused by the J2 perturbation for Earth and Mars orbiters, and estimating the uncertainty in an asteroids gravitational field. Simulations are presented which indicate that the observer can accurately estimate both the periodic nature of these perturbations as well as the magnitudes. Nomenclature A = System dynamics matrix C = Output matrix , a e e = Estimation error in states

Low-Thrust Control of a Lunar Mapping Orbit

A method is presented for establishing and maintaining a lunar mapping orbit using continuous-low-thrust propulsion. Optimal control theory is used to maintain a lunar orbit that is low-altitude, near-polar, and sun-synchronous, which are three typical requirements for a successful lunar mapping mission. The analysis of the optimal control problem leads to the commonly seen two-point boundary-value problem, which is solved using a simple indirect shooting algorithm. Simulations are presented for a one-year mapping duration, in which it is shown that an average control force of 0.5 N for a 1000-kg-class spacecraft is required to rotate the orbit plane at the sun-synchronous rate. Because this amounts to a total A V of roughly 15 km/s, a fairly large propellant mass of 416 kg would be required from a typical ion thruster for a one-year mission. However, if the science requirements can be fulfilled in a shorter 1―2-month mission, the required propellant mass could be drastically reduced. Also, it is shown that if the desired control accuracy of the sun-synchronous ascending node is relaxed, the required thrust levels can be decreased by roughly 0.2 N.

OPTIMAL CONTROL OF A SUN-SYNCHNOROUS LUNAR ORBITER

Optimal control of a spacecraft orbiting the Moon in a Sun-synchronous orbit that provides consistent illuminati on and efficient imaging for mapping is investigated in this paper. The perturbations due to the gravitational force from the Earth, Sun and the non-spherical gravity field of the Moon are utilized as a framework for deriving the equations of motion of the spacecraft. The spacecraft position is controlled to maintain a consta nt semimajor axis, eccentricity, inclination and argument of periapsis with the ascending node changing at a Sun-synchronous rate. A nonlinear model is developed that describes the dynamics of the system and then this model is converted into a line ar-like structure. This nonlinear dynamic problem is then solved by employing an optimal nonlinear control approach, known as the State Dependent Algebraic Riccati Equation i.e. the SDRE technique. Control accelerations are found using the SDRE approach to maintain the spacecraft in the desired orbit. An interesting approximate closed form solution that makes the control implementation simple is found after tracking the change in the control gains obtained from the SDRE technique. Numerical results are presented and analyzed.