Weight Optimization in H∞ Loop-Shaping Control and Applications

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Abstract

The primary objective of this thesis is to leverage on the framework of H∞ loop-shaping control to formulate efficient and powerful optimization algorithms in LMI framework for the synthesis of performance loop-shaping weights. The H∞ loop-shaping design procedure is an efficient controller synthesis technique that combines classical loop-shaping concepts with H∞ synthesis. This procedure establishes a good tradeoff between robust stability and robust performance of a closed-loop system in a systematic manner. However, the selection of pre- and/or post-compensators, a crucial step in the design procedure, is nontrivial as factors such as the right half plane poles/zeros of the nominal plant, roll-off rate around the crossover frequency, strength of cross-coupling in multi-input multi-output systems, expected bandwidth, etc. must be adequately considered.Firstly, a frequency-dependent weight optimization framework is formulated in state-space form in order to remove the dependency on frequency while retaining the objective of maximizing the robust stability margin of a closed-loop system. This formulation facilitates the synthesis of low-order controllers, which is desirable from an implementation perspective.A weight optimization framework that incorporates smoothness constraints in order to prevent the cancellation of important modes of the system, for example, lightly damped poles/zeros of flexible structures, is subsequently formulated. The proposed formulation is intuitive from a design perspective as the smoothness constraints are expressed as gradient constraints on a log-log scale in dB/decade, consistent with the notation used in Bode plot for single-input single-output systems and singular value plots for multi-input multi-output systems.Thereafter, an optimization framework that maximizes the robust performance of a closed-loop system is presented. The philosophy in this framework is in line with practical design objectives that give the best achievable robust performance on a particular problem once a level of robust stability margin is demanded.Lastly, a novel unmanned vehicle is proposed. The vehicle uses a full six-degree-of-freedom tri-rotor actuation, capable of fully decoupled thrust and torque vectoring in all the 3D space. This vehicle can act as an unmanned ground vehicle or unmanned aerial vehicle, but the objective herein is restricted to the upright stability of the vehicle while operating on the ground as this is a precursor to rolling motion. The full nonlinear model of the vehicle is derived and linearized for subsequent controller synthesis, and this is thereafter validated by means of numerical simulations.

Keyword(s)

H∞ Loop-Shaping Control; LMI; Robust Control; Unmanned Vehicle; Weight Synthesis

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