Nonlinear Estimation and Control Methods for Mechanical and Aerospace Systems under Actuator Uncertainty

Air flow velocity field control is of crucial importance in aerospace applications to prevent the potentially destabilizing effects of phenomena such as cavity ow oscillations, flow separation, flow-induced limit cycle oscillations (LCO) (flutter), vorticity, and acoustic instabilities. Flow control is also important in aircraft applications to reduce drag in aircraft wings for improved flight performance. Although passive flow control approaches are often utilized due to their simplicity, active flow control (AFC) methods can achieve improved flight performance over a wider range of time-varying operating conditions by automatically adjusting their level of control actuation in response to real-time sensor measurements. Although several methods for AFC have been presented in recent literature, there remain numerous challenges to be overcome in closed-loop nonlinear AFC design. Additional challenges arise in control design for practical systems with limited onboard sensor measurements and uncertain actuator dynamics. In this thesis, robust nonlinear control methods are developed, which are rigorously proven to achieve reliable control of fluid flow systems under uncertain, time-varying operating conditions and actuator model uncertainty. Further, to address the practical control design challenges resulting from sensor limitations, this thesis research will investigate and develop new methods of sliding mode estimation, which are shown to achieve finite-time state estimation for systems with limited onboard sensing capabilities. The specific contributions presented in this thesis include: 1) the application of proper orthogonal decomposition (POD)-based model order reduction techniques to develop simplified, control-oriented mathematical models of actuated fluid flow dynamic systems; 2) the rigorous development of nonlinear closed-loop active flow control techniques to achieve asymptotic regulation of fluid flow velocity fields; 3) the design of novel sliding mode estimation and control methods to regulate fluid flow velocity fields in the presence of actuator uncertainty; 4) the design of a nonlinear control method that achieves simultaneous fluid flow velocity control and LCO suppression in a flexible airfoil; and 5) the analysis of a discontinuous hierarchical sliding mode estimation method using a differential inclusions-based technique

Adaptive Nonlinear Regulation Control of Thermoacoustic Oscillations in Rijke-Type Systems

Adaptive nonlinear control of self-excited oscillations in Rijke-type thermoacoustic systems is considered. To demonstrate the methodology, a well-accepted thermoacoustic dynamic model is introduced, which includes arrays of sensors and monopole-like actuators. To facilitate the derivation of the adaptive control law, the dynamic model is recast as a set of nonlinear ordinary differential equations, which are amenable to control design. The control-oriented nonlinear model includes unknown, unmeasurable, nonvanishing disturbances in addition to parametric uncertainty in both the thermoacoustic dynamic model and the actuator dynamic model. To compensate for the unmodeled disturbances in the dynamic model, a robust nonlinear feedback term is included in the control law. One of the primary challenges in the control design is the presence of input-multiplicative parametric uncertainty in the dynamic model for the control actuator. This challenge is mitigated through innovative algebraic manipulation in the regulation error system derivation along with a Lyapunov-based adaptive control law. To address practical implementation considerations, where sensor measurements of the complete state are not available for feedback, a detailed analysis is provided to demonstrate that system observability can be ensured through judicious placement of pressure (and/or velocity) sensors. Based on this observability condition, a sliding-mode observer design is presented, which is shown to estimate the unmeasurable states using only the available sensor measurements. A detailed Lyapunov-based stability analysis is provided to prove that the proposed closed-loop active thermoacoustic control system achieves asymptotic (zero steady-state error) regulation of multiple thermoacoustic modes in the presence of the aforementioned model uncertainty. Numerical Monte Carlo-type simulation results are also provided, which demonstrate the performance of the proposed closed-loop control system under various sets of operating conditions

Adaptive Modified RISE-based Quadrotor Trajectory Tracking with Actuator Uncertainty Compensation

This paper presents an adaptive robust nonlinear control method, which achieves reliable trajectory tracking control for a quadrotor unmanned aerial vehicle in the presence of gyroscopic effects, rotor dynamics, and external disturbances. Through novel mathematical manipulation in the error system development, the quadrotor dynamics are expressed in a control-oriented form, which explicitly incorporates the uncertainty in the gyroscopic term and control actuation term. An adaptive robust nonlinear control law is then designed to stabilize both the position and attitude loops of the quadrotor system. A rigorous Lyapunov-based analysis is utilized to prove asymptotic trajectory tracking, where the region of convergence can be made arbitrarily large through judicious control gain selection. Moreover, the stability analysis formally addresses gyroscopic effects and actuator uncertainty. To illustrate the performance of the control law, comparative numerical simulation results are provided, which demonstrate the improved closed-loop performance achieved under varying levels of parametric uncertainty and disturbance magnitudes

Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control

Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control

Adaptive Modified RISE-based Quadrotor Trajectory Tracking with Actuator Uncertainty Compensation

This paper presents an adaptive robust nonlinear control method, which achieves reliable trajectory tracking control for a quadrotor unmanned aerial vehicle in the presence of gyroscopic effects, rotor dynamics, and external disturbances. Through novel mathematical manipulation in the error system development, the quadrotor dynamics are expressed in a control-oriented form, which explicitly incorporates the uncertainty in the gyroscopic term and control actuation term. An adaptive robust nonlinear control law is then designed to stabilize both the position and attitude loops of the quadrotor system. A rigorous Lyapunov-based analysis is utilized to prove asymptotic trajectory tracking, where the region of convergence can be made arbitrarily large through judicious control gain selection. Moreover, the stability analysis formally addresses gyroscopic effects and actuator uncertainty. To illustrate the performance of the control law, comparative numerical simulation results are provided, which demonstrate the improved closed-loop performance achieved under varying levels of parametric uncertainty and disturbance magnitudes

Robust and Adaptive Nonlinear Regulation of Thermoacoustic Oscillations in Rijke-Type Systems

Nonlinear control of self-excited oscillations in a Rijke-type thermoacoustic system is considered. A commonly used thermoacoustic model with a number of monopole-like actuators is first introduced. The model is expressed in a nonlinear control-oriented form, which includes unmodeled nonlinearities and parametric uncertainty in both the thermoacoustic dynamics and in the actuator dynamics. A robust and adaptive nonlinear control law is developed to compensate for the parametric uncertainty and unmodeled nonlinearities. Challenges in the control design include input-multiplicative parametric uncertainty. This challenge is mitigated through careful algebraic manipulation in the regulation error system development along with a Lyapunov-based adaptive law. A rigorous Lyapunov-based stability analysis is used to prove that the nonlinear controller achieves asymptotic regulation of an uncertain thermoacoustic system with multiple modes

Robust Nonlinear Estimation and Control of Fluid Flow Velocity Fields

A proper orthogonal decomposition (POD)-based model reduction technique is utilized to develop a closed-loop nonlinear flow control system. By using POD, the Navier-Stokes partial differential equations are recast as a set of nonlinear ordinary differential equations in terms of the unknown Galerkin coefficients. A sliding mode estimator is then employed to estimate, in finite time, the unknown coefficients in the reduced-order model for the actuated flow system. The estimated coefficients are utilized as feedback measurements in a robust nonlinear control law. A rigorous analysis is utilized to analyze the convergence of the sliding mode estimator, and a Lyapunov-based stability analysis is used to prove asymptotic regulation of the flow field velocity to a desired velocity profile. The control objective of tracking a desired velocity profile presented here is a proof of concept only; the proposed methodology could be applied to various flow control objectives. Numerical simulation results are provided to demonstrate the capability of the estimator/control system to regulate the velocity of the flow field to a desired state

A Closed-Loop Nonlinear Control and Sliding Mode Estimation Strategy for Fluid Flow Regulation

Novel sliding mode observer (SMO) and robust nonlinear control methods are presented, which are shown to achieve finite-time state estimation and asymptotic regulation of a fluid flow system. To facilitate the design and analysis of the closed-loop active flow control (AFC) system, proper orthogonal decomposition–based model order reduction is utilized to express the Navier-Stokes partial differential equations as a set of nonlinear ordinary differential equations. The resulting reduced-order model contains a measurement equation that is in a nonstandard mathematical form.This challenge is mitigated through the detailed design and analysis of an SMO. The observer is shown to achieve finite-time estimation of the unmeasurable states of the reduced-order model using direct sensor measurements of the flow field velocity.The estimated states are utilized as feedback measurements in a closed-loop AFC system. To address the practical challenge of actuator bandwidth limitations, the control law is designed to be continuous. A rigorous Lyapunov-based stability analysis is presented to prove that the closed-loop flow estimation and control method achieves asymptotic regulation of a fluid flow field to a prescribed state. Numerical simulation results are also provided to demonstrate the performance of the proposed closed-loop AFC system, comparing 2 different designs for the SMO