A new approach to nonlinear feedback control for suppressing periodic disturbances: Part 1. Fundamental Theory

A new nonlinear feedback control approach is proposed in the present study to suppress periodic exogenous disturbances based on a frequency domain theory of nonlinear systems. In Part 1 of this paper, a series of fundamental theoretical results and techniques are established. It is shown that a low order nonlinear feedback may be sufficient for some control problems. A general procedure is then proposed for controller design. The new approach is demonstrated by a case study on the design of an active vibration control system in Part 2. Theoretical analysis and simulation results verify the effectiveness of the new results

Advances In Internal Model Principle Control Theory

In this thesis, two advanced implementations of the internal model principle (IMP) are presented. The first is the identification of exponentially damped sinusoidal (EDS) signals with unknown parameters which are widely used to model audio signals. This application is developed in discrete time as a signal processing problem. An IMP based adaptive algorithm is developed for estimating two EDS parameters, the damping factor and frequency. The stability and convergence of this adaptive algorithm is analyzed based on a discrete time two time scale averaging theory. Simulation results demonstrate the identification performance of the proposed algorithm and verify its stability. The second advanced implementation of the IMP control theory is the rejection of disturbances consisting of both predictable and unpredictable components. An IMP controller is used for rejecting predictable disturbances. But the phase lag introduced by the IMP controller limits the rejection capability of the wideband disturbance controller, which is used for attenuating unpredictable disturbance, such as white noise. A combination of open and closed-loop control strategy is presented. In the closed-loop mode, both controllers are active. Once the tracking error is insignificant, the input to the IMP controller is disconnected while its output control action is maintained. In the open loop mode, the wideband disturbance controller is made more aggressive for attenuating white noise. Depending on the level of the tracking error, the input to the IMP controller is connected intermittently. Thus the system switches between open and closed-loop modes. A state feedback controller is designed as the wideband disturbance controller in this application. Two types of predictable disturbances are considered, constant and periodic. For a constant disturbance, an integral controller, the simplest IMP controller, is used. For a periodic disturbance with unknown frequencies, adaptive IMP controllers are used to estimate the frequencies before cancelling the disturbances. An extended multiple Lyapunov functions (MLF) theorem is developed for the stability analysis of this intermittent control strategy. Simulation results justify the optimal rejection performance of this switched control by comparing with two other traditional controllers

Robust Control Methods for Nonlinear Systems with Uncertain Dynamics and Unknown Control Direction

Robust nonlinear control design strategies using sliding mode control (SMC) and integral SMC (ISMC) are developed, which are capable of achieving reliable and accurate tracking control for systems containing dynamic uncertainty, unmodeled disturbances, and actuator anomalies that result in an unknown and time-varying control direction. In order to ease readability of this dissertation, detailed explanations of the relevant mathematical tools is provided, including stability denitions, Lyapunov-based stability analysis methods, SMC and ISMC fundamentals, and other basic nonlinear control tools. The contributions of the dissertation are three novel control algorithms for three different classes of nonlinear systems: single-input multipleoutput (SIMO) systems, systems with model uncertainty and bounded disturbances, and systems with unknown control direction. Control design for SIMO systems is challenging due to the fact that such systems have fewer actuators than degrees of freedom to control (i.e., they are underactuated systems). While traditional nonlinear control methods can be utilized to design controllers for certain classes of cascaded underactuated systems, more advanced methods are required to develop controllers for parallel systems, which are not in a cascade structure. A novel control technique is proposed in this dissertation, which is shown to achieve asymptotic tracking for dual parallel systems, where a single scalar control input directly affects two subsystems. The result is achieved through an innovative sequential control design algorithm, whereby one of the subsystems is indirectly stabilized via the desired state trajectory that is commanded to the other subsystem. The SIMO system under consideration does not contain uncertainty or disturbances. In dealing with systems containing uncertainty in the dynamic model, a particularly challenging situation occurs when uncertainty exists in the input-multiplicative gain matrix. Moreover, special consideration is required in control design for systems that also include unknown bounded disturbances. To cope with these challenges, a robust continuous controller is developed using an ISMC technique, which achieves asymptotic trajectory tracking for systems with unknown bounded disturbances, while simultaneously compensating for parametric uncertainty in the input gain matrix. The ISMC design is rigorously proven to achieve asymptotic trajectory tracking for a quadrotor system and a synthetic jet actuator (SJA)-based aircraft system. In the ISMC designs, it is assumed that the signs in the uncertain input-multiplicative gain matrix (i.e., the actuator control directions) are known. A much more challenging scenario is encountered in designing controllers for classes of systems, where the uncertainty in the input gain matrix is extreme enough to result in an a priori-unknown control direction. Such a scenario can result when dealing with highly inaccurate dynamic models, unmodeled parameter variations, actuator anomalies, unknown external or internal disturbances, and/or other adversarial operating conditions. To address this challenge, a SMCbased self-recongurable control algorithm is presented, which automatically adjusts for unknown control direction via periodic switching between sliding manifolds that ultimately forces the state to a converging manifold. Rigorous mathematical analyses are presented to prove the theoretical results, and simulation results are provided to demonstrate the effectiveness of the three proposed control algorithms

Adaptive rejection of finite band disturbances - theory and applications

Le chapitre présente les techniques de rejection adpative de perturbation inconnue mais de bande finie. Plusieurs exemples sont mentionnés et l'application au rejet adaptatifs de perturbation inconnues sur une suspension active est décrite en détailThe techniques for adaptive rejection of unknown finite band disturbances are reviewed. Several applications are mentionned and the application to the adaptive rejection of unknown disturbances on an active suspension is presented in detail

Direct Adaptive Control for Stability and Command Augmentation System of an Air-Breathing Hypersonic Vehicle

In this paper we explore a Direct Adaptive Control scheme for stabilizing a non-linear, physics based model of the longitudinal dynamics for an air breathing hypersonic vehicle. The model, derived from first principles, captures the complex interactions between the propulsion system, aerodynamics, and structural dynamics. The linearized aircraft dynamics show unstable and non-minimum phase behavior. It also shows a strong short period coupling with the fuselage-bending mode. The value added by direct adaptive control and the theoretical requirements for stable convergent operation is displayed. One of the main benefits of the Directive Adaptive Control is that it can be implemented knowing very little detail about the plant. The implementation uses only measured output feedback to accomplish the adaptation. A stability analysis is conducted on the linearized plant to understand the complex aero-propulsion and structural interactions. The multivariable system possesses certain characteristics beneficial to the adaptive control scheme; we discuss these advantages and ideas for future work