Integrated Optimal and Robust Control of Spacecraft in Proximity Operations

With the rapid growth of space activities and advancement of aerospace science and technology, many autonomous space missions have been proliferating in recent decades. Control of spacecraft in proximity operations is of great importance to accomplish these missions. The research in this dissertation aims to provide a precise, efficient, optimal, and robust controller to ensure successful spacecraft proximity operations. This is a challenging control task since the problem involves highly nonlinear dynamics including translational motion, rotational motion, and flexible structure deformation and vibration. In addition, uncertainties in the system modeling parameters and disturbances make the precise control more difficult. Four control design approaches are integrated to solve this challenging problem. The first approach is to consider the spacecraft rigid body translational and rotational dynamics together with the flexible motion in one unified optimal control framework so that the overall system performance and constraints can be addressed in one optimization process. The second approach is to formulate the robust control objectives into the optimal control cost function and prove the equivalency between the robust stabilization problem and the transformed optimal control problem. The third approach is to employ the è-D technique, a novel optimal control method that is based on a perturbation solution to the Hamilton-Jacobi-Bellman equation, to solve the nonlinear optimal control problem obtained from the indirect robust control formulation. The resultant optimal control law can be obtained in closedorm, and thus facilitates the onboard implementation. The integration of these three approaches is called the integrated indirect robust control scheme. The fourth approach is to use the inverse optimal adaptive control method combined with the indirect robust control scheme to alleviate the conservativeness of the indirect robust control scheme by using online parameter estimation such that adaptive, robust, and optimal properties can all be achieved. To show the effectiveness of the proposed control approaches, six degree-offreedom spacecraft proximity operation simulation is conducted and demonstrates satisfying performance under various uncertainties and disturbances

Modelling and control of a twin rotor MIMO system.

In this research, a laboratory platform which has 2 degrees of freedom (DOF), the Twin Rotor MIMO System (TRMS), is investigated. Although, the TRMS does not fly, it has a striking similarity with a helicopter, such as system nonlinearities and cross-coupled modes. Therefore, the TRMS can be perceived as an unconventional and complex "air vehicle" that poses formidable challenges in modelling, control design and analysis and implementation. These issues are the subject of this work. The linear models for 1 and 2 DOFs are obtained via system identification techniques. Such a black-box modelling approach yields input-output models with neither a priori defined model structure nor specific parameter settings reflecting any physical attributes. Further, a nonlinear model using Radial Basis Function networks is obtained. Such a high fidelity nonlinear model is often required for nonlinear system simulation studies and is commonly employed in the aerospace industry. Modelling exercises were conducted that included rigid as well as flexible modes of the system. The approach presented here is shown to be suitable for modelling complex new generation air vehicles. Modelling of the TRMS revealed the presence of resonant system modes which are responsible for inducing unwanted vibrations. In this research, open-loop, closed-loop and combined open and closed-loop control strategies are investigated to address this problem. Initially, open-loop control techniques based on "input shaping control" are employed. Digital filters are then developed to shape the command signals such that the resonance modes are not overly excited. The effectiveness of this concept is then demonstrated on the TRMS rig for both 1 and 2 DOF motion, with a significant reduction in vibration. The linear model for the 1 DOF (SISO) TRMS was found to have the non-minimum phase characteristics and have 4 states with only pitch angle output. This behaviour imposes certain limitations on the type of control topologies one can ado·pt. The LQG approach, which has an elegant structure with an embedded Kalman filter to estimate the unmeasured states, is adopted in this study. The identified linear model is employed in the design of a feedback LQG compensator for the TRMS with 1 DOF. This is shown to have good tracking capability but requires. high control effort and has inadequate authority over residual vibration of the system. These problems are resolved by further augmenting the system with a command path prefilter. The combined feedforward and feedback compensator satisfies the performance objectives and obeys the constraint on the actuator. Finally, 1 DOF controller is implemented on the laboratory platform