The method of controlled Lagrangians is an energy shaping control technique for underactuated Lagrangian systems. Energy shaping control design methods are appealing as they retain the underlying nonlinear dynamics and can provide stability results that hold over larger domain than can be obtained using linear design and analysis. The objective of this dissertation is to identify the control challenges in applying the method of controlled Lagrangians to practical engineering problems and to suggest ways to enhance the closed-loop performance of the controller. This dissertation describes a procedure for incorporating artificial gyroscopic forces in the method of controlled Lagrangians. Allowing these energy-conserving forces in the closed-loop system provides greater freedom in tuning closed-loop system performance and expands the class of eligible systems. In energy shaping control methods, physical dissipation terms that are neglected in the control design may enter the system in a way that can compromise stability. This is well illustrated through the "ball on a beam" example. The effect of physical dissipation on the closed-loop dynamics is studied in detail and conditions for stability in the presence of natural damping are discussed. The control technique is applied to the classic "inverted pendulum on a cart" system. A nonlinear controller is developed which asymptotically stabilizes the inverted equilibrium at a specific cart position for the conservative dynamic model. The region of attraction contains all states for which the pendulum is elevated above the horizontal plane. Conditions for asymptotic stability in the presence of linear damping are developed. The onlinear controller is validated through experiments. Experimental cart damping is best modeled using static and Coulomb friction. Experiments show that static and Coulomb friction degrades the closed-loop performance and induces limit cycles. A Lyapunov-based switching controller is proposed and successfully implemented to suppress the limit cycle oscillations. The Lyapunov-based controller switches between the energy shaping nonlinear controller, for states away from the equilibrium, and a well-tuned linear controller, for states close to the equilibrium. The method of controlled Lagrangians is applied to vehicle systems with internal moving point mass actuators. Applications of moving mass actuators include certain spacecraft, atmospheric re-entry vehicles, and underwater vehicles. Control design using moving mass actuators is challenging; the system is often underactuated and multibody dynamic models are higher dimensional. We consider two examples to illustrate the application of controlled Lagrangian formulation. The first example is a spinning disk, a simplified, planar version of a spacecraft spin stabilization problem. The second example is a planar, streamlined underwater vehicle. / Ph. D.

Many landing sites of scientific interest on Mars including most of the Southern Hemisphere at elevations above 2km Mars Orbiter Laser Altimeter reference are inaccessible due to current limitations in precision entry guidance and payload deceleration. Precision guidance and large payload deceleration is challenging due to the thin Martian atmosphere, large changes in free stream conditions during entry, and aerothermal and aerodynamic instability concerns associated with control systems with direct external flow field interaction. Such risks have descoped past Mars missions to unguided entry with the exception of Mars Science Laboratory's (MSL) bank angle guidance. Consequently, prior to MSL landing ellipses were on the order of 100's of km. MSL has approached the upper limit of payload deceleration capability for rigid, blunt body sphere cone aeroshells used on all successful Mars entry missions. Hypersonic Inflatable Aerodynamic Decelerators (HIADS) are in development for larger payload deceleration capability through inflated aeroshell diameters greater than rigid aeroshells constrained by the launch rocket diameter, but to date there has been limited dynamics, control, and guidance development for their use on future missions. This dissertation develops internal moving mass actuator (IMMA) control systems for improving Mars precision entry guidance of rigid capsules and demonstrating precision guidance capability for HIADs. IMMAs provide vehicle control moments without direct interaction with the external flow field and can increase payload mass delivered through reducing propellant mass for control and using portions of the payload for the IMMAs. Dynamics models for entry vehicles with rotation and translation IMMAs are developed. IMMA control systems using the models are developed for two NASA vehicle types: a 2.65 m, 602 kg Mars Phoenix-sized entry capsule and an 8.3 m, 5.9 metric ton HIAD approaching payload requirements for robotic precursor missions for future human missions. Linear Quadratic controllers with integral action for guidance command tracking are developed for translation and rotation IMMA configurations. Angle of attack and sideslip guidance laws are developed as an alternative to bank angle guidance for decoupling range and cross-range control for improved precision entry guidance. A new variant of the Apollo Earth return terminal guidance algorithm is implemented to provide the closed-loop angle of attack range control commands. Nonlinear simulations of the entire 8 degree of freedom closed-loop systems demonstrate precision guidance to nominal trajectories and final targets for off-nominal initial entry conditions for flight path angle, range, cross-range, speed and attitude. Mechanical power studies for IMMA motion show rotation IMMA require less total mechanical power than translation actuators, but both systems have low nominal mechanical power requirements (below 100 Watts). Precision guidance for both systems to terminal targets greater than 38 km down-range from an open-loop ballistic entry is shown for low mechanical power, low CM displacement, (< 4.5 in) and at low internal velocities (< 2 in/s) over significant dynamic pressure changes. The collective precision guidance results and low mechanical power requirements show IMMA based entry guidance control systems constitute a promising alternative to thruster based control systems for future Mars landers. / Ph. D.