Warren N. White

A direct Lyapunov approach for a class of underactuated mechanical systems

A Lyapunov direct method is proposed for a class of underactuated, mechanical systems. The direct method is derived in general for systems having n degrees of freedom of which only m < n are actuated. The applications consist of a class of systems where the elements of the mass/inertia matrix and the gravitational forces/torques are either constants or functions of a single generalized position variable and where n is two and m is one. The time derivative of the candidate Lyapunov function produces a relation that is solved via a matching method. Some of the matching equations consist of linear differential and partial differential equations. It is shown for this class of systems, that the solutions of these linear differential and partial differential equations necessary for assuring asymptotic stability can be evaluated numerically as part of the feedback process. Examples are presented involving an inverted pendulum cart and an inertia wheel pendulum

Control of a double inverted pendulum with hydraulic actuation: a case study

A hydraulic actuated inverted pendulum with controller is designed, built, and tested. There are several objectives behind the device development. The first objective is to create an apparatus that can be used for class exercises for upper level control courses. Specifically, the device can be used to illustrate the complete control design process from plant modeling and identification to controller selection, design, and implementation, The next objective is to create a test bed for control theory investigations. The last objective is to choose an important means of actuation that does not receive significant coverage in the controls literature. We present details of the pendulum construction, its dynamic model, and controller design. The steps taken to model the plant and actuator together with the identification procedure present a useful example for control students regarding other aspects of control design which are not often covered in control texts.

Simulation of Electromechanical Interactions of Permanent-Magnet Direct-Drive Wind Turbines Using the FAST Aeroelastic Simulator

Two detailed models of permanent-magnet direct-drive (PMDD) wind turbines with full converters are presented in this paper: one for a 10-kW turbine, and one for a 5-MW turbine. The models are verified by comparing the power curves found through simulation with field test data. Other results are also presented that show the unprecedented detail of the models. The mathematical representations include switching models for the full converters, circuit models for permanent-magnet synchronous generators, realistic aerodynamics, tower and blade vibrations, and many other variables. The models are valuable tools for wind turbine design and research and can be used for a wide range of purposes including control system design, sensitivity analysis, and interactions between the electrical and mechanical parts of a PMDD wind turbine. Simulation of the models is carried out in the MATLAB/Simulink environment using the FAST aeroelastic simulator.

Wind Turbine Power Capture Control With Robust Estimation

A robust control scheme to optimize the power capture of a wind turbine is proposed. A novel identification technique is used both to estimate the unknown aerodynamic properties and to regulate the turbine speed. A Lyapunov-based approach is adopted to choose the set point change direction so that power capture can be maximized for the given wind speed and environmental parameters. The set point consists of the turbine tip speed ratio and the turbine blade pitch. The efficacy of the controller is demonstrated through simulation.

A Maximum Power Tracking Technique for Grid-Connected DFIG-Based Wind Turbines

In this paper, a maximum power tracking technique is presented for doubly fed induction generator-based wind turbines. The presented technique is a novel version of the conventional method, i.e., the electrical torque is proportional to the square of the rotor speed, in which the proportional coefficient is adaptively adjusted in real-time through three control laws. The first control law calculates the desired electrical torque using feedback linearization, assuming that the power capture coefficient and the desired rotor speed are instantaneously identified. The second control law estimates the real-time values of the power capture coefficient from a Lyapunov-based analysis, and the third control law provides the desired rotor speed. These control laws cause the turbine to adaptively adjust the rotor speed toward a desired speed in which the operating point moves in the direction of increasing the power capture coefficient. The proposed maximum power tracking method differs distinctly from the perturb-and-observe scheme by eliminating a need for adding a dither or perturbation signal, and robustly tracks the trajectory of maximum power points even in the event of a sudden wind speed change that can cause the perturb-and-observe technique to fail. In this paper, the National Renewal Energy Laboratory 5-MW reference wind turbine model is used to demonstrate the validity and robustness of the proposed method.

A Direct Lyapunov Approach for Stabilization of Underactuated Mechanical Systems

Control of underactuated systems is treated from a Lyapunov direct method approach. The method results in a set of three matching conditions, the solution of which is easily accomplished. The method developed is capable of treating more complicated systems than that reported in an earlier publication. The suitability of the Lyapunov candidate function is demonstrated through mathematical proofs. An application of the method to the ball and beam is presented.

Matching and digital control implementation for underactuated systems

This paper describes two problems related to the digital implementation of control laws in the infinite dimensional family of matching control laws, namely state estimation and sampled data induced error. The entire family of control laws is written for an inverted pendulum cart. Numerical simulations which include sampled data and a state estimator are presented for one of the control laws in this family.

The presentation of Lagrange's equations in introductory robotics courses

The topic of Lagranges dynamic equations is presented in a fashion suitable for introductory robotics courses. The development of the material does not rely on either principles of virtual work or variational calculus. The thrust of the demonstration is that, given dynamic for a rigid body, one can always manipulate the equations to show that the equations depend exclusively on the difference between the total kinetic and potential energies of the system. >

Improvements in direct Lyapunov stabilization of underactuated, mechanical systems

A Lyapunov direct method is presented for the stabilization of underactuated, mechanical systems. The Lyapunov approach provides the tools for control law design. This work represents a continued development of previously published techniques. The major contribution of the presentation is that a method is demonstrated for assuring the positive definiteness of certain matrices associated with the formulation. A stabilization example using the rotary inverted pendulum is included.

Region II wind power capture maximization using robust control and estimation with alternating gradient search

A two-fold control method is proposed consisting of a nonlinear robust controller working in conjunction with an extremum seeking gradient search controller. The robust controller provides stable control of the rotor angular velocity while also producing an estimation of the hard to measure and nonlinear aerodynamic torque provided by the wind. The gradient search method uses the estimate to update the tipspeed ratio and blade pitch which will drive the system in the direction of increasing turbine power capture. The efficacy of the control method is demonstrated through simulation in the presence of a realistic wind signal and measurement noise in the wind velocity feedback.