FILTERED-DYNAMIC-INVERSION CONTROL FOR UNKNOWN MINIMUM-PHASE SYSTEMS WITH UNKNOWN RELATIVE DEGREE

We present filtered-dynamic-inversion (FDI) control for unknown linear time-invariant systems that are multi-input multi-output and minimum phase with unknown-but-bounded relative degree. This FDI controller requires limited model information, specifically, knowledge of an upper bound on the relative degree and knowledge of the first nonzero Markov parameter. The FDI controller is a single-parameter high-parameter-stabilizing controller that is robust to uncertainty in the relative degree. We characterize the stability of the closed-loop system. We present numerical examples, where the FDI controller is implemented in feedback with mathematical and physical systems. The numerical examples demonstrate that the FDI controller for unknown relative degree is effective for stabilization, command following, and disturbance rejection. We demonstrate that for a sufficiently large parameter, the average power of the closed-loop performance is arbitrarily small

SPECIFIED MOTION AND FEEDBACK CONTROL OF ENGINEERING STRUCTURES WITH DISTRIBUTED SENSORS AND ACTUATORS

This dissertation addresses the control of flexible structures using distributed sensors and actuators. The objective to determine the required distributed actuation inputs such that the desired output is obtained. Two interrelated facets of this problem are considered. First, we develop a dynamic-inversion solution method for determining the distributed actuation inputs, as a function of time, that yield a specified motion. The solution is shown to be useful for intelligent structure design, in particular, for sizing actuators and choosing their placement. Secondly, we develop a new feedback control method, which is based on dynamic inversion. In particular, filtered dynamic inversion combines dynamic inversion with a low-pass filter, resulting in a high-parameter-stabilizing controller, where the parameter gain is the filter cutoff frequency. For sufficiently large parameter gain, the controller stabilizes the closed-loop system and makes the L2-gain of the performance arbitrarily small, despite unknown-and-unmeasured disturbances. The controller is considered for both linear and nonlinear structural models

State-Space Interpretation of Model Predictive Control

A model predictive control technique based on a step response model is developed using state estimation techniques. The standard step response model is extended so that integrating systems can be treated within the same framework. Based on the modified step response model, it is shown how the state estimation techniques from stochastic optimal control can be used to construct the optimal prediction vector without introducing significant additional numerical complexity. In the case of integrated or double integrated white noise disturbances filtered through general first-order dynamics and white measurement noise, the optimal filter gain is parametrized explicitly in terms of a single parameter between 0 and 1, thus removing the requirement for solving a Riccati equation and equipping the control system with useful on-line tuning parameters. Parallels are drawn to the existing MPC techniques such as Dynamic Matrix Control (DMC), Internal Model Control (IMC) and Generalized Predictive Control (GPC)

FILTERED-DYNAMIC-INVERSION CONTROL FOR FIXED-WING UNMANNED AERIAL SYSTEMS

Instrumented umanned aerial vehicles represent a new way of measuring turbulence in the atmospheric boundary layer. However, autonomous measurements require control methods with disturbance-rejection and altitude command-following capabilities. Filtered dynamic inversion is a control method with desirable disturbance-rejection and command-following properties, and this controller requires limited model information. We implement filtered dynamic inversion as the pitch controller in an altitude-hold autopilot. We design and numerically simulate the continuous-time and discrete-time filtered-dynamic-inversion controllers with anti-windup on a nonlinear aircraft model. Finally, we present results from a flight experiment comparing the filtered-dynamic-inversion controller to a classical proportional-integral controller. The experimental results show that the filtered-dynamic-inversion controller performs better than a proportional-integral controller at certain values of the parameter

DISCRETE-TIME ADAPTIVE CONTROL ALGORITHMS FOR REJECTION OF SINUSOIDAL DISTURBANCES

We present new adaptive control algorithms that address the problem of rejecting sinusoids with known frequencies that act on an unknown asymptotically stable linear time-invariant system. To achieve asymptotic disturbance rejection, adaptive control algorithms of this dissertation rely on limited or no system model information. These algorithms are developed in discrete time, meaning that the control computations use sampled-data measurements. We demonstrate the effectiveness of algorithms via analysis, numerical simulations, and experimental testings. We also present extensions to these algorithms that address systems with decentralized control architecture and systems subject to disturbances with unknown frequencies

Anti-Disturbance Compensation-Based Nonlinear Control for a Class of MIMO Uncertain Nonlinear Systems

Multi-Inputs-Multi-Outputs (MIMO) systems are recognized mainly in industrial applications with both input and state couplings, and uncertainties. The essential principle to deal with such difficulties is to eliminate the input couplings, then estimate the remaining issues in real-time, followed by an elimination process from the input channels. These difficulties are resolved in this research paper, where a decentralized control scheme is suggested using an Improved Active Disturbance Rejection Control (IADRC) configuration. A theoretical analysis using a state-space eigenvalue test followed by numerical simulations on a general uncertain nonlinear highly coupled MIMO system validated the effectiveness of the proposed control scheme in controlling such MIMO systems. Time-domain comparisons with the Conventional Active Disturbance Rejection Control (CADRC)-based decentralizing control scheme are also included

On Observer-Based Control of Nonlinear Systems

Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented