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

Optimal sliding mode controllers for attitude tracking of spacecraft

This paper studies two optimal sliding mode control laws using integral sliding mode control (ISM) for some spacecraft attitude tracking problems. Integral sliding mode control combining the first order sliding mode and optimal control is applied to quaternion-based spacecraft attitude tracking manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state dependent Riccati equation (SDRE) and Control Lyapunov function (CLF) approaches are used to solve the infinite-time nonlinear optimal problem. The second method of Lyapunov is used to show that tracking is achieved globally. An example of multiaxial attitude tracking manoeuvres is presented and simulation results are included to verify the usefulness of these controllers

Fast Adaptive Robust Differentiator Based Robust-Adaptive Control of Grid-Tied Inverters with a New L Filter Design Method

In this research, a new nonlinear and adaptive state feedback controller with a fast-adaptive robust differentiator is presented for grid-tied inverters. All parameters and external disturbances are taken as uncertain in the design of the proposed controller without the disadvantages of singularity and over-parameterization. A robust differentiator based on the second order sliding mode is also developed with a fast-adaptive structure to be able to consider the time derivative of the virtual control input. Unlike the conventional backstepping, the proposed differentiator overcomes the problem of explosion of complexity. In the closed-loop control system, the three phase source currents and direct current (DC) bus voltage are assumed to be available for feedback. Using the Lyapunov stability theory, it is proven that the overall control system has the global asymptotic stability. In addition, a new simple L filter design method based on the total harmonic distortion approach is also proposed. Simulations and experimental results show that the proposed controller assurances drive the tracking errors to zero with better performance, and it is robust against all uncertainties. Moreover, the proposed L filter design method matches the total harmonic distortion (THD) aim in the design with the experimental result

Adaptive Backstepping Controller Design for Stochastic Jump Systems

In this technical note, we improve the results in a paper by Shi et al., in which problems of stochastic stability and sliding mode control for a class of linear continuous-time systems with stochastic jumps were considered. However, the system considered is switching stochastically between different subsystems, the dynamics of the jump system can not stay on each sliding surface of subsystems forever, therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this technical note, the backstepping techniques are adopted to overcome the problem in a paper by Shi et al.. The resulting closed-loop system is bounded in probability. It has been shown that the adaptive control problem for the Markovian jump systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. A numerical example is given to show the potential of the proposed techniques

Integrated control and estimation based on sliding mode control applied to electrohydraulic actuator

Many problems in tracking control have been identified over the years, such as the availability of systems states, the presence of noise and system uncertainties, and speed of response, just to name a few. This thesis is concerned with developing novel integrated control and estimation algorithms to overcome some of these problems in order to achieve an efficient tracking performance. Since there are some significant advantages associated with Sliding Mode Control (SMC) or Variable Structure Control (VSC), (fast regulation rate and robustness to uncertainties), this research reviews and extends new filtering concepts for state estimation, referred to as the Variable Structure Filter (VSF)and Smooth Variable Structure Filter (SVSF). These are based on the philosophy of Sliding Mode Control.The VSF filter is designed to estimate some of the states of a plant when noise and uncertainties are presented. This is accomplished by refining an estimate of the states in an iterative fashion using two filter gains, one based on a noiseless system with no uncertainties and the second gain which reflects these uncertainties. The VSF is combined “seamlessly” with the Sliding Mode Controller to produce an integrated controller called a Sliding Mode Controller and Filter (SMCF). This new controller is shown to be a robust and effective integrated control strategy for linear systems. For nonlinear systems, a novel integrated control strategy called the Smooth Sliding Mode Controller and Filter (SSMCF), fuses the SMC and SVSF in a particular form to address nonlinearities. The gain term in the SVSF is redefined to form a new algorithm called the “SVSF with revised gain” in order to obtain a better estimation performance. Its performance is compared to that of the Extended Kalman Filter (EKF) when applied to a particular nonlinear plant.The SMCF and SSMCF are applied to the experimental prototype of a precision positioning hydraulic system called an ElectroHydraulic Actuator (EHA) system. The EHA system is known to display nonlinear characteristics but can approximate linear behavior under certain operating conditions, making it ideal to test the robustness of the proposed controllers.The main conclusion drawn in this research was that the SMCF and SSMCF as developed and implemented, do exhibit robust and high performance state estimation and trajectory tracking control given modeling uncertainties and noise. The controllers were applied to a prototype EHA which demonstrated the use of the controllers in a “real world” application. It was also concluded that the application of the concepts of VSC for the controller can alleviate a challenging mechanical problem caused by a slip-stick characteristic in friction. Another conclusion is that the revised form of the SVSF could obtain robust and fast state estimation for nonlinear systems.The original contributions of the research include: i) proposing the SMCF and SSMCF, ii) applying the Sliding Mode Controller to suppress cross-over oscillations caused by the slip-stick characteristics in friction which often occur in mechanical systems, iii) the first application of the SVSF for state estimation and iv) a comparative study of the SVSF and Extended Kalman Filter (EKF) to the EHA demonstrating the superiority of the SVSF for state estimation performance under both steady-state and transient conditions for the application considered.The dissertation is written in a paper format unlike the traditional Ph.D thesis manuscript. The content of the thesis discourse is based on five manuscripts which are appended at the end of the thesis. Fundamental principles and concepts associated with SMC, VSF, SVSF and the fused controllers are introduced. For each paper, the objectives, approaches, typical results, conclusions and major contributions are presented. Major conclusions are summarized and original contributions reiterated

Feedback linearization of nonminimum phase systems and control of aeroelastic systems and undersea vehicles

The thesis presents the design of feedback control systems for a class of nonminimum phase single input-single output nonlinear systems. The linearized system is assumed to have one unstable zero. Since asymptotic or exact tracking of output trajectory cannot be accomplished, an approximate output is derived by neglecting the unstable zero. Based on the inversion of the new input-output map, a feedback linearizing control is derived; These results are applied to control an aeroelastic system and a small undersea vehicle. For pitch angle control and plunge motion regulation, an inverse control system is designed for the aeroelastic system. Simulation results are shown for the pitch controller and the design is found to be robust to variation in the parameters. Dive plane control of an undersea vehicle is accomplished using an inverse control law. To attenuate the effect of the surface waves, a servocompensator has been designed. Later, a controller is also designed using the sliding mode control technique, to make the system more robust

A Novel Fuzzy Logic Based Adaptive Supertwisting Sliding Mode Control Algorithm for Dynamic Uncertain Systems

This paper presents a novel fuzzy logic based Adaptive Super-twisting Sliding Mode Controller for the control of dynamic uncertain systems. The proposed controller combines the advantages of Second order Sliding Mode Control, Fuzzy Logic Control and Adaptive Control. The reaching conditions, stability and robustness of the system with the proposed controller are guaranteed. In addition, the proposed controller is well suited for simple design and implementation. The effectiveness of the proposed controller over the first order Sliding Mode Fuzzy Logic controller is illustrated by Matlab based simulations performed on a DC-DC Buck converter. Based on this comparison, the proposed controller is shown to obtain the desired transient response without causing chattering and error under steady-state conditions. The proposed controller is able to give robust performance in terms of rejection to input voltage variations and load variations.Comment: 14 page