Analysis of the theta-D filter as applied to hit-to-kill interceptors and satellite orbit determination

When designing feedback control systems, there is often a need for estimation methods that provide system information that is not readily available via sensors placed within the system. In many cases a sensor that measures a particular system state either does not exist or is prohibitively expensive. In addition, all realistic systems contain some degree of nonlinearity. This thesis focuses on two such cases: missile guidance with bearings-only measurements and GPS satellite orbit determination. In each case, a new nonlinear filter, the [theta]-D method, is used and evaluated for its performance in providing the necessary estimation. To aid the filter in the bearings-only application, a guidance law is formulated that assists the filter in estimating the target location despite the lack of range measurement. An implementation procedure, called the Staggered Filter Concept, is also presented for implementing a continuous filter, such as the [theta]-D filter, with measurements taken at discrete intervals. This procedure is used to implement the orbit determination algorithm on the Missouri S&T Satellite Team M-SAT mission --Abstract, page iii

Nonlinear Control and Estimation with General Performance Criteria

This dissertation is concerned with nonlinear systems control and estimation with general performance criteria. The purpose of this work is to propose general design methods to provide systematic and effective design frameworks for nonlinear system control and estimation problems. First, novel State Dependent Linear Matrix Inequality control approach is proposed, which is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. By solving a state dependent linear matrix inequality at each time step, the sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this dissertation unify existing results on nonlinear quadratic regulator, Hinfinity and positive real control. Secondly, an H2-Hinfinity State Dependent Riccati Equation controller is proposed in this dissertation. By solving the generalized State Dependent Riccati Equation, the optimal control solution not only achieves the optimal quadratic regulation performance, but also has the capability of external disturbance reduction. Numerically efficient algorithms are developed to facilitate effective computation. Thirdly, a robust multi-criteria optimal fuzzy control of nonlinear systems is proposed. To improve the optimality and robustness, optimal fuzzy control is proposed for nonlinear systems with general performance criteria. The Takagi-Sugeno fuzzy model is used as an effective tool to control nonlinear systems through fuzzy rule models. General performance criteria have been used to design the controller and the relative weighting matrices of these criteria can be achieved by choosing different coefficient matrices. The optimal control can be achieved by solving the LMI at each time step. Lastly, since any type of controller and observer is subject to actuator failures and sensors failures respectively, novel robust and resilient controllers and estimators are also proposed for nonlinear stochastic systems to address these failure problems. The effectiveness of the proposed control and estimation techniques are demonstrated by simulations of nonlinear systems: the inverted pendulum on a cart and the Lorenz chaotic system, respectively

The constrained discrete-time state-dependent Riccati equation technique for uncertain nonlinear systems

The objective of the thesis is to introduce a relatively general nonlinear controller/estimator synthesis framework using a special type of the state-dependent Riccati equation technique. The continuous time state-dependent Riccati equation (SDRE) technique is extended to discrete-time under input and state constraints, yielding constrained (C) discrete-time (D) SDRE, referred to as CD-SDRE. For the latter, stability analysis and calculation of a region of attraction are carried out. The derivation of the D-SDRE under state-dependent weights is provided. Stability of the D-SDRE feedback system is established using Lyapunov stability approach. Receding horizon strategy is used to take into account the constraints on D-SDRE controller. Stability condition of the CD-SDRE controller is analyzed by using a switched system. The use of CD-SDRE scheme in the presence of constraints is then systematically demonstrated by applying this scheme to problems of spacecraft formation orbit reconfiguration under limited performance on thrusters. Simulation results demonstrate the efficacy and reliability of the proposed CD-SDRE. The CD-SDRE technique is further investigated in a case where there are uncertainties in nonlinear systems to be controlled. First, the system stability under each of the controllers in the robust CD-SDRE technique is separately established. The stability of the closed-loop system under the robust CD-SDRE controller is then proven based on the stability of each control system comprising switching configuration. A high fidelity dynamical model of spacecraft attitude motion in 3-dimensional space is derived with a partially filled fuel tank, assumed to have the first fuel slosh mode. The proposed robust CD-SDRE controller is then applied to the spacecraft attitude control system to stabilize its motion in the presence of uncertainties characterized by the first fuel slosh mode. The performance of the robust CD-SDRE technique is discussed. Subsequently, filtering techniques are investigated by using the D-SDRE technique. Detailed derivation of the D-SDRE-based filter (D-SDREF) is provided under the assumption of Gaussian noises and the stability condition of the error signal between the measured signal and the estimated signals is proven to be input-to-state stable. For the non-Gaussian distributed noises, we propose a filter by combining the D-SDREF and the particle filter (PF), named the combined D-SDRE/PF. Two algorithms for the filtering techniques are provided. Several filtering techniques are compared with challenging numerical examples to show the reliability and efficacy of the proposed D-SDREF and the combined D-SDRE/PF

Hybrid Control Strategies for Rapid, Large Angle Satellite Slew Maneuvers

This research investigated hybrid control strategies for rapid satellite pointing. First, a detailed computer simulation model of AFIT\u27s SIMSAT satellite simulator was constructed. Control strategies were developed to enable the system to perform large-angle, 3-axis slewing maneuvers using a combination of both thrusters and reaction wheels. To handle the non-linear model, a State Dependent Riccati Equation controller was programmed and successfully controlled the computer-modeled satellite for any given slewing maneuver. A simpler PD controller was then programmed and demonstrated on the computer simulation of SIMSAT, using a combination of thruster and reaction wheel control inputs for large-angle single axis maneuvers and for small angles using three-axis control. There was good agreement between the experimentally obtained maneuver results and those produced with the computer simulation model for the single-axis case. Lastly, the trade-off between settling time and thruster fuel is discussed, as well as the variation of gains required to achieve maximum performance for a desired slew

Advanced control designs for output tracking of hydrostatic transmissions

The work addresses simple but efficient model descriptions in a combination with advanced control and estimation approaches to achieve an accurate tracking of the desired trajectories. The proposed control designs are capable of fully exploiting the wide operation range of HSTs within the system configuration limits. A new trajectory planning scheme for the output tracking that uses both the primary and secondary control inputs was developed. Simple models or even purely data-driven models are envisaged and deployed to develop several advanced control approaches for HST systems

Optimal Control of a Large Space Telescope Using an Annular Momentum Control Device

Application of a new development in the field of momentum storage devices, the Annular Momentum Control Device (AMCD), to the twin problems of large angle maneuvers and fine pointing control is considered. The basic concept of the AMCD consists of a spinning rim, with no central hub area, suspended by a minimum of three magnetic bearings, and driven by a noncontacting electromagnetic spin motor. The dissertation considers in detail the design of an optimal controller to achieve both large angle maneuvers and the fine pointing control of a Large Telescope (LST) with a single configuration, consisting of a single AMCD mounted in a single gimbal