• active structural control
• Bode plots
• flexible margins
• flexible modes
• gain-phase stabilization
• linear and nonlinear controllers comparison
• Nichols chart
• rigid modes
• spurious mode

NASA's Asteroid Redirect Robotic Mission (ARRM) aims to pick up a boulder from of a large asteroid and transport it to a distant retrograde orbit around the Moon for future exploration by a manned mission. The main goal of ARRM is to grab an uncertain boulder, which size may be even ten times the size of the spacecraft, with two robotic arms and assure extremely accurate maneuvers to properly complete all the phases present in the timeline of the mission. In this thesis, a detailed analysis for one of the main control challenges in ARRM is described, i.e., the design of a three-axis attitude control of the ARRM spacecraft with the captured boulder in the presence of large uncertainties in the physical model of the boulder.
A 30 degree-of-freedom nonlinear dynamic model of the ARRM spacecraft and boulder combination is first presented. Then, this nonlinear model about the nominal operating conditions to study the system's modal properties is linearized. A finite element model of the ARRM spacecraft and boulder combination is used to validate the lumped linear dynamic model. A third dynamic model, the SD Fast one, is then presented. The implementation of a third model is necessary to carry out simulations with a large saving in terms of computational time.
Successively, a control law design phase is performed. The design and the tuning of a controller are made by using the previous linearized dynamic models. An appropriate controller requires the system composed by the spacecraft and the boulder to maintain the desired attitude for the entire mission. The linear and nonlinear control laws for the attitude control problem are implemented with specific methods. For the linear control algorithm, a frequency-response method has been followed; for the nonlinear control law, a qualitative procedure with computational simulations has been implemented. Both the proportional-derivative based linear controller with lead-lag compensator and roll-off filter and the robust nonlinear tracking control law that tracks a derivative plus proportional-derivative based desired attitude trajectory give robust performance over the range of boulder parameters. They are indeed, simulated in nominal and non-nominal scenarios to quantify their performance.
A detailed comparison between the two designed controllers is presented. The comparison utilizes the main concepts of generalized gain and phase margins to overcome the impossibility of using the common phase and gain margin in nonlinear control. It was finally demonstrated that the nonlinear control law performed greatly also in onerous scenarios, such as slew maneuver in presence of extremely large angles.