| Model-Error Control Synthesis employs an optimal real-time nonlinear estimator to determine model-error corrections to the control input of a nominal controller using either a one time-step ahead prediction, an approximate receding-horizon optimization, or a modified approximate receding-horizon optimization technique. Control compensation is achieved by using the estimated model-error as a signal synthesis adaptive correction to the nominal control input so that maximum performance is achieved in the face of bounded model uncertainty and disturbance inputs. The proof of the closed loop stability is derived using a Padé approximation for the time delay. A robust stability analysis using the interlacing property from the Hermite-Biehler theorem is also presented. As a result, systematic robust control designs and analysis procedures are developed.; Model-Error Control Synthesis is applied to a simple mass-damper-spring system and a non-minimum phase unstable system. From these linear systems the relations between the optimization methods and the physical parameters, i.e., the damping factor and the position of a non-minimum phase zero relative to a unstable pole, are found. In addition the design and analysis steps are applied to two nonlinear multi-input multi-output systems. They include spacecraft attitude maneuvers with attitude-angle measurements only, i.e., without any angular-velocity measurements, and control of limit cycle oscillations in an aeroelastic system with pitch angle and plunge displacement measurements only, i.e., without any velocity measurements. For these nonlinear examples, with the assumption of norm bounded nonlinear uncertainty, we show that the closed loop systems are the globally quadratically stable. |
