David G. Wilson

Robust adaptive backstepping control for a nonholonomic mobile robot

This paper introduces a robust adaptive control architecture for nonholonomic mobile robots. The concept of backstepping provides a bridge between the kinematics and dynamics. In previous work normally only the vehicle steering, dependent upon the kinematics are considered for vehicle control. Improved tracking performance is achieved by including vehicle dynamics and robustness compensation for variances in parameters. Numerical simulations demonstrate the effectiveness of the robust adaptive control algorithm.

Exergy and irreversible entropy production thermodynamic concepts for nonlinear control design

This paper develops a novel nonlinear control system design methodology that uniquely combines: concepts from exergy and entropy; Hamiltonian systems; Lyapunovs direct method and optimal analysis; and power flow control analysis. Relationships are derived between exergy/entropy and Lyapunov optimal functions for Hamiltonian systems based on the recognition that the Hamiltonian is stored exergy. The control system stability and performance are partitioned and evaluated based on exergy generation and exergy dissipation terms. This control methodology results in both necessary and sufficient conditions for stability of a class of nonlinear systems as a result of the application of the second law of thermodynamics to the time derivative of the Hamiltonian. The methodology is demonstrated with numerical simulation examples.

Augmented Sliding Mode Control for Flexible Link Manipulators

A method of sliding mode control (SMC) is proposed for the control of flexible, nonlinear, and structural systems. The method departs from standard sliding mode control by dispensing with generalized accelerations during the control law design. Global, asymptotic stability of rigid body motion is maintained if knowledge on the bounds of the neglected terms exists. Furthermore, this method provides damping for the measured flexible body modes. This paper investigates an augmented SMC technique for slewing flexible manipulators. A conventional sliding surface uses a first order system including a combination of error and error rate terms. The augmented sliding surface includes an enhanced term that helps to reject flexible degrees-of-freedom. The algorithms are theoretically developed and experimentally tested on a slewing single flexible link robot. The test apparatus is instrumented with a strain gauge at the root and an accelerometer attached at the tip. A DC motor and encoder are used to servo the link from an initial position to a final position. A standard cubic polynomial is employed to generate the reference trajectories. The augmented SMC algorithm showed improved performance by reducing the flexible link tip oscillations.

What is a limit cycle

A limit cycle is the stability boundary for linear and non-linear control systems. Hamiltonian mechanics and power flow control are employed to demonstrate this property of limit cycles. The presentation begins with the concept of linear limit cycles which is extended to non-linear limit cycles. Many examples are used to demonstrate these concepts including linear and non-linear oscillators, power engineering, and an extension to a class of plane differential systems. Power flow control based on Hamiltonian mechanics is shown to be applicable to a large class of non-linear systems. Finally, eigenanalysis and flight stability for linear systems are extended to non-linear systems and is referred to as ‘the power flow principle of stability for non-linear systems’.

Active Aerodynamic Blade Distributed Flap Control Design Procedure for Load Reduction on the UpWind 5MW Wind Turbine

This paper develops a system identification approach and procedure that is employed for distributed control system design for large wind turbine load reduction applications. The primary goal of the study is to identify the process that can be used with multiple sensor inputs of varying types (such as aerodynamic or structural) that can be used to construct state-space models compatible with MIMO modern control techniques (such as LQR, LQG, H1, robust control, etc.). As an initial step, this study employs LQR applied to multiple flap actuators on each blade as control inputs and local deflection rates at the flap spanwise locations as measured outputs. Future studies will include a variety of other sensor and actuator locations for both design and analysis with respect to varying wind conditions (such as high turbulence and gust) to help reduce structural loads and fatigue damage. The DU SWAMP aeroservoelastic simulation environment is employed to capture the complexity of the control design scenario. The NREL 5MW UpWind reference wind turbine provides the large wind turbine dynamic characteristics used for the study. Numerical simulations are used to demonstrate the feasibility of the overall approach. This study shows that the distributed controller design can provide load reductions for turbulent wind profiles that represent operation in above-rated power conditions.

Renewable energy microgrid control with energy storage integration

The goal of this paper is to present the design of feedback controllers for the integration of renewable energy into a DC bus microgrid. These feedback controllers are divided into two types. The first type is based on a feedback guidance command that implements the boost converter duty cycle. The second type is based on Hamiltonian Surface Shaping and Power Flow Control (HSSPFC) [1], [2], [3], [4] that implements the energy storage systems. The duty cycle controller is fully coupled while the HSSPFC is completely decoupled due to the skew-symmetric form that is analogous to spacecraft attitude and robot manipulator controllers. A DC bus with two boost converters and an equivalent load is used as an example. Numerical simulation results show the effects of 0% energy storage with renewable energy supplies to 100% energy storage with fossil energy supplies.

Exergy and Entropy Thermodynamic Concepts for Control System Design: Slewing Single Axis

This paper develops a novel control system design methodology that uniquely combines: concepts from thermodynamic exergy and entropy; Hamiltonian systems; Lyapunov’s direct method and Lyapunov optimal analysis; electric AC power concepts; and power flow analysis. Relationships are derived between exergy/entropy and Lyapunov optimal functions for Hamiltonian systems. The methodology is demonstrated with a few fundamental numerical simulation examples that are related to spacecraft gimbal regulation and slewing control: 1) a rotary mass-spring-damper dynamic system that employs PID regulator control; 2) a Dung oscillator/Coulomb friction nonlinear model that employs PID regulator control; and 3) a linear PID tracking control design for the rotary mass-spring-damper system. The control system performances are partitioned and evaluated based on exergy generation and exergy dissipation terms. This novel nonlinear control methodology results in both necessary and sucient conditions for stability of nonlinear systems.

Collective systems:physical and information exergies.

Collective systems are typically defined as a group of agents (physical and/or cyber) that work together to produce a collective behavior with a value greater than the sum of the individual parts. This amplification or synergy can be harnessed by solving an inverse problem via an information-flow/communications grid: given a desired macroscopic/collective behavior find the required microscopic/individual behavior of each agent and the required communications grid. The goal of this report is to describe the fundamental nature of the Hamiltonian function in the design of collective systems (solve the inverse problem) and the connections between and values of physical and information exergies intrinsic to collective systems. In particular, physical and information exergies are shown to be equivalent based on thermodynamics and Hamiltonian mechanics.

Exergy and Irreversible Entropy Production Thermodynamic Concepts for Control Design: Nonlinear Systems

This paper develops a novel control system design methodology that uniquely combines: concepts from thermodynamic exergy and entropy; Hamiltonian systems; Lyapunovs direct method and Lyapunov optimal analysis; electric AC power concepts; and power flow analysis. Relationships are derived between exergy/entropy and Lyapunov optimal functions for Hamiltonian systems. The methodology is demonstrated with two fundamental numerical simulation examples: 1) a Duffing oscillator/Coulomb friction nonlinear model that employs PID regulator control and 2) a van der Pol nonlinear oscillator system. The control system performances and/or appropriately identified terms are partitioned and evaluated based on exergy generation and exergy dissipation terms. This novel nonlinear control methodology results in both necessary and sufficient conditions for stability of nonlinear systems

Evaluation of three model reference adaptive control algorithms for robotic manipulators

This paper evaluates three model reference adaptive control (MRAC) schemes for completing a telerobotic task. The three proposed schemes are evaluated for accurate trajectory control of a general three-degree-of-freedom robotic manipulator, in the presence of large payload variations, and modeling inaccuracies. The three MRAC schemes evaluated are: (1) Computed-torque method, which uses the nonlinear dynamic model of the robot in the control formulation and Popovs hyperstability criteria, (2) independent joint control method, which uses decoupled linear dynamic equations in the control formulation and based on Popovs hyperstability criteria, and (3) independent joint control method based on sensitivity analysis. Computer simulations of a three-degree-of-freedom manipulator, with a large payload and fast maneuver are used to analyze the performance of the three schemes. The investigation shows the robustness of the computed-torque method when compared to the independent joint schemes.