Lyapunov-based Control Design For Uncertain Mimo Systems

In this dissertation. we document the progress in the control design for a class of MIMO nonlinear uncertain system from five papers. In the first part, we address the problem of adaptive control design for a class of multi-input multi-output (MIMO) nonlinear systems. A Lypaunov based singularity free control law, which compensates for parametric uncertainty in both the drift vector and the input gain matrix, is proposed under the mild assumption that the signs of the leading minors of the control input gain matrix are known. Lyapunov analysis shows global uniform ultimate boundedness (GUUB) result for the tracking error under full state feedback (FSFB). Under the restriction that only the output vector is available for measurement, an output feedback (OFB) controller is designed based on a standard high gain observer (HGO) stability under OFB is fostered by the uniformity of the FSFB solution. Simulation results for both FSFB and OFB controllers demonstrate the efcacy of the MIMO control design in the classical 2-DOF robot manipulator model. In the second part, an adaptive feedback control is designed for a class of MIMO nonlinear systems containing parametric uncertainty in both the drift vector and the input gain matrix, which is assumed to be full-rank and non-symmetric in general. Based on an SDU decomposition of the gain matrix, a singularity-free adaptive tracking control law is proposed that is shown to be globally asymptotically stable (GAS) under full-state feedback. iii Output feedback results are facilitated via the use of a high-gain observer (HGO). Under output feedback control, ultimate boundedness of the error signals is obtained the size of the bound is related to the size of the uncertainty in the parameters. An explicit upper bound is also provided on the size of the HGO gain constant. In third part, a class of aeroelastic systems with an unmodeled nonlinearity and external disturbance is considered. By using leading- and trailing-edge control surface actuations, a full-state feedforward/feedback controller is designed to suppress the aeroelastic vibrations of a nonlinear wing section subject to external disturbance. The full-state feedback control yields a uniformly ultimately bounded result for two-axis vibration suppression. With the restriction that only pitching and plunging displacements are measurable while their rates are not, a high-gain observer is used to modify the full-state feedback control design to an output feedback design. Simulation results demonstrate the ef cacy of the multi-input multioutput control toward suppressing aeroelastic vibration and limit cycle oscillations occurring in pre and post utter velocity regimes when the system is subjected to a variety of external disturbance signals. Comparisons are drawn with a previously designed adaptive multi-input multi-output controller. In the fourth part, a continuous robust feedback control is designed for a class of high-order multi-input multi-output (MIMO) nonlinear systems with two degrees of freedom containing unstructured nonlinear uncertainties in the drift vector and parametric uncertainties in the high frequency gain matrix, which is allowed to be non-symmetric in general. Given some mild assumptions on the system model, a singularity-free continuous robust tracking coniv trol law is designed that is shown to be semi-globally asymptotically stable under full-state feedback through a Lyapunov stability analysis. The performance of the proposed algorithm have been verified on a two-link robot manipulator model and 2-DOF aeroelastic model

MIMO nonlinear PID predictive controller

A class of nonlinear generalised predictive controllers (NGPC) is derived for multi-input multi-output (MIMO) nonlinear systems with offset or steady-state response error. The MIMO composite controller consists of an optimal NGPC and a nonlinear disturbance observer. The design of the nonlinear disturbance observer to estimate the offset is particularly simple, as is the associated proof of overall nonlinear closed-loop system stability. Moreover, the transient error response of the disturbance observer can be arbitrarily specified by simple design parameters. Very satisfactory performance of the proposed MIMO nonlinear predictive controller is demonstrated for a three-link nonlinear robotic manipulator example

Fault detection and isolation of malicious nodes in MIMO Multi-hop Control Networks

A MIMO Multi-hop Control Network (MCN) consists of a MIMO LTI system where the communication between sensors, actuators and computational units is supported by a (wireless) multi-hop communication network, and data flow is performed using scheduling and routing of sensing and actuation data. We provide necessary and sufficient conditions on the plant dynamics and on the communication protocol configuration such that the Fault Detection and Isolation (FDI) problem of failures and malicious attacks to communication nodes can be solved.Comment: 6 page

Identification of linear systems by an asymptotically stable observer

A formulation is presented for the identification of a linear multivariable system from single or multiple sets of input-output data. The system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded eigenvalue assignment procedure. The prescribed eigenvalues for the observer may be real, complex, mixed real and complex, or zero. In this formulation, the Markov parameters of the observer are identified from input-output data. The Markov parameters of the actual system are then recovered from those of the observer and used to obtain a state space model of the system by standard realization techniques. The basic mathematical formulation is derived, and extensive numerical examples using simulated noise-free data are presented to illustrate the proposed method

Active vibration damping of the Space Shuttle remote manipulator system

The feasibility of providing active damping augmentation of the Space Shuttle Remote Manipulator System (RMS) following normal payload handling operations is investigated. The approach used in the analysis is described, and the results for both linear and nonlinear performance analysis of candidate laws are presented, demonstrating that significant improvement in the RMS dynamic response can be achieved through active control using measured RMS tip acceleration data for feedback