The design of controllers subject to the nonlinear H-infinity criterion is explored. The plants to be controlled are the attitude motion of spacecraft, subject to some disturbance torque. Two cases are considered: the regulation about an inertially-fixed direction, and an Earth-pointing spacecraft in a circular orbit, subject to the gravity-gradient torque. The spacecraft attitude is described using the modified Rodrigues parameters. A series of controllers are designed using the nonlinear H-infinity control criterion, and are subsequently generated using a Taylor series expansion to approximate solutions of the relevant Hamilton-Jacobi equations. The controllers are compared, using both input-output and initial condition simulations. A proof is used to demonstrate that the linearized controller solves the H-infinity control problem for the inertial pointing problem when describing the plant using the modified Rodrigues parameters.

The design of controllers subject to the nonlinear H-infinity criterion is explored. The plants to be controlled are the attitude motion of spacecraft, subject to some disturbance torque. Two cases are considered: the regulation about an inertially-fixed direction, and an Earth-pointing spacecraft in a circular orbit, subject to the gravity-gradient torque. The spacecraft attitude is described using the modified Rodrigues parameters. A series of controllers are designed using the nonlinear H-infinity control criterion, and are subsequently generated using a Taylor series expansion to approximate solutions of the relevant Hamilton-Jacobi equations. The controllers are compared, using both input-output and initial condition simulations. A proof is used to demonstrate that the linearized controller solves the H-infinity control problem for the inertial pointing problem when describing the plant using the modified Rodrigues parameters.

This dissertation develops a general framework for designing stabilizing feedback controllers and observers for dynamics with state/time dependent gains on the control signals and measured outputs. These gains have potential singularity periods but satisfy a technically non-trivial condition referred to as persistence of excitation. A persistence filter design constitutes the primary theoretical innovation of this work around which the controller and observer development is centered. Application areas of singular gain systems considered in this study include robotics, biomechanics, intelligent structures and spacecrafts. Several representative problems involving singular, time-dependent gains are addressed. The specific contributions of this dissertation are outlined as follows: (i) a stabilizing feedback for linear, single-input systems with time-varying, singular control scaling is designed that allows arbitrary exponential convergence rate for the closed-loop dynamics. An adaptive control generalization of this result allows asymptotic convergence in presence of unknown plant parameters. An extension to a special, single-input nonlinear system in the controller canonical form is also proposed. It is proven that this control design results in bounded tracking error signals for a trajectory tracking objective; (ii) observer design for linear, single-output systems with time-varying, singular measurement gains is considered. A persistence filter similar in structure to the control counterpart aids an observer design that guarantees exponential state reconstruction with arbitrary convergence rates; (iii) the observer and controller designs are combined to obtain an exponentially stabilizing output feedback controller for linear, single-input, single-output dynamics with singular gains on both the control and measurements. A novel separation property is established as a consequence. The construction motivates applications to stabilization with reversible transducers which can switch between sensor and actuator modes. The results are verified on two illustrative applications, vibration control using piezoelectric devices and inverted pendulum stabilization with a DC motor. The linear result is further generalized to include state dependent gains; (iv) application of the persistence filter theory to spacecraft attitude stabilization using intermittent actuation is explored. The intermittence is characterized by a time-varying, periodically singular control gain. A nonlinear persistence filter allows construction of an exponentially stabilizing controller and simulations verify convergence with intermittent actuation where conventional proportional-derivative control fails; (v) a stabilization result for a special multi-input, linear system with time-varying matrix control gains is presented. The matrix gain is assumed to be diagonal but allows fewer controls than states subject to a controllability assumption in absence of the singular gain matrix. The single-input adaptive control results are shown to extend to the multi-input case. An application to angular velocity stabilization of an underactuated rigid spacecraft is considered. / text

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.

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This dissertation addresses novel techniques in determining gyroless micro-satellite attitude and attitude rate. The main objective of this thesis is to explore the possibility of using commercially available low cost micro-light star sensor as a stand-alone sensor for micro-satellite attitude as well as attitude rate determination. The objective is achieved by developing accurate and computationally efficient algorithms for the realization of onboard operation of a low fidelity star sensor. All the algorithms developed here are tested with the measurement noise presented in the catalog of the sensor array STAR-1000. A novel accurate second order sliding mode observer (SOSMO) is designed for discrete time uncertain linear multi-output system. Our design procedure is effective for both matched and unmatched bounded uncertain ties and/or disturbances. The bound on uncertainties and/or disturbances is assumed to be unknown. This problem is addressed in this work using the second order multiple sliding modes approach. Second order sliding manifold and corresponding sliding condition for discrete time system is defined similar on the lines of continuous counterpart. Our design is not restricted to a particular class of uncertain (matched) discrete time system. Moreover, it can handle multiple outputs unlike single out-put systems. The observer design is achieved by driving the state observation error and its first order finite difference to the vicinity of the equilibrium point (0,0) in a finite steps and maintaining them in the neighborhood thereafter. The estimation synthesis is based on Quasi Sliding Mode (QSM) design. The problem of designing sliding mode observer for a linear system subjected to unknown inputs requires observer matching condition. This condition is needed to ensure that the state estimation error is a asymptotically stable and is independent of the unknown input during the sliding motion. In the absence of a matching condition, asymptotic stability of the reduced order error dynamics on the sliding surface is not guaranteed. However, unknown bounded inputs guarantee bounded error on state estimation. The QSM design guarantees an ultimate error bound by incorporating Boundary Layer (BL) in its design procedure. The observer achieves one order of magnitude improvement in estimation accuracy than the conventional sliding mode observer (SMO) design for an unknown input. The observer estimation errors, satisfying the given stability conditions, converge to an ultimate finite bound (with in the specified BL) of O(T2), where T Is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The robustness of the proposed observer with respect to measurement noise is also analyzed. The design algorithm is very simple to apply and is implemented for two examples with different classes of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results show the robustness with respect to the measurement noise for SOSMO. Second order sliding mode observer gain can be calculated off-line and the same gain can work for large band of disturbance as long as the disturbance acting on the continuous time system is bounded and smooth. The SOSMO is simpler to implement on board compared to the other traditional nonlinear filters like Pseudo-Linear-Kalman-filter(PLKF); Extended Kalman Filter(EKF). Moreover, SMO possesses an automatic adaptation property same as optimal state estimator(like Kalman filter) with respect to the intensity of the measurement noise. The SMO rejects the noisy measurements automatically, in response to the increased noise intensity. The dynamic performance of the observer on the sliding surface can be altered and no knowledge of noise statistics is required. It is shown that the SOSMO performs more accurately than the PLKF in application to micro-satellite angular rate estimation since PLKF is not an optimal filter. A new method for estimation of satellite angular rates through derivative approach is proposed. The method is based on optic flow of star image patterns formed on a star sensor. The satellite angular rates are derived directly from the 2D-coordinates of star images. Our algorithm is computationally efficient and requires less memory allocation compared to the existing vector derivative approaches, where there is also no need for star identification. The angular rates are computed using least square solution method, based on the measurement equation obtained by optic flow of star images. These estimates are then fed into discrete time second order sliding mode observer (SOSMO). The performance of angular rate estimation by SOSMO is compared with the discrete time First order SMO and PLKF. The SOSMO gives the best estimates as compared to the other two schemes in estimating micro-satellite angular rates in all three axes. The improvement in accuracy is one order of magnitude (around1.7984 x 10−5 rad/ sec,8.9987 x 10−6 rad/ sec and1.4222 x 10−5 rad/ sec in three body axes respectively) in terms of standard deviation in steady state estimation error. A new method and algorithm is presented to determine star camera parameters along with satellite attitude with high precision even if these parameters change during long on-orbit operation. Star camera parameters and attitude need to be determined independent of each other as they both can change. An efficient, closed form solution method is developed to estimate star camera parameters (like focal length, principal point offset), lens distortions (like radial distortion) and attitude. The method is based on a two step procedure. In the first step, all parameters (except lens distortion) are estimated using a distortion free camera model. In the second step, lens distortion coefficient is estimated by linear least squares (LS) method. Here the derived camera parameters in first step are used in the camera model that incorporates distortion. However, this method requires identification of observed stars with the catalogue stars. But, on-orbit star identification is difficult as it utilizes the values of camera calibrating parameters that can change in orbit(detector and optical element alignment get change in orbit due to solar pressure or sudden temperature change) from the ground calibrated value. This difficulty is overcome by employing a camera self-calibration technique which only requires four observed stars in three consecutive image frames. Star camera parameters along with lens (radial and decentering) distortion coefficients are determined by camera self calibration technique. Finally Kalman filter is used to refine the estimated data obtained from the LS based method to improve the level of accuracy. We consider the true values of camera parameters as (u0,v0) = (512.75,511.25) pixel, f = 50.5mm; The ground calibrated values of those parameters are (u0,v0) =( 512,512) pixel, f = 50mm; Worst case radial distortion coefficient affecting the star camera lens is considered to be k1 =5 x 10−3 .Our proposed method of attitude determination achieves accuracy of the order of magnitude around 6.2288 x 10−5 rad,3.3712 x 10−5 radand5.8205 x 10−5 rad in attitude angles φ,θ and ψ. Attitude estimation by existing methods in the literature diverges from the true value since they utilize the ground calibrated values of camera parameters instead of true values. To summarize, we developed a formal theory of discrete time Second Order Sliding Mode Observer for uncertain multi-output system. Our methods achieve the desired accuracy while estimating satellite attitude and attitude rate using low fidelity star sensor data. Our methods require lower on-board processing requirement and less memory allocation; thus are suitable for micro-satellite applications. Thus, the objective of using low fidelity star sensor as stand-alone sensor in micro-satellite application is achieved.