Control, stability analysis and grid integration of wind turbines.

In Chapters 2 and 3 of the thesis we propose a self-scheduled control method for a doublyfed induction generator driven by a wind turbine (DFIGWT), whose rotor is connected to the power grid via two back-to-back PWM power converters. We design a controller for this system using the linear matrix inequality based approach to linear parameter varying (LPV) systems, which takes into account the nonlinear dynamics of the system. We propose a two-loop hierarchical control structure. The inner-loop current controller, which considers the synchronous speed and the generator rotor speed as a parameter vector, achieves robust tracking of the rotor current reference signals. The outer-loop electrical torque controller aims for wind energy capture maximization, grid frequency support and generates the reference rotor current. We perform a controller reduction for the inner-loop LPV controller, which is not doable by conventional model-reduction techniques, because the controller is parameter-dependent. In simulation, the reduced order controller has been tested on a nonlinear 4th order DFIG model with a two-mass model for the drive-train. Stability and high performances have been achieved over the entire operating range of the DFIGWT. More importantly, simulation results have demonstrated the capability and contribution of the proposed two-loop control systems to grid frequency support. In Chapter 4 we investigate the integral input-to-state stability (iISS) property for passive nonlinear systems. We show that under mild assumptions, a passive nonlinear system which is globally asymptotically stable is also iISS. Moreover, the integral term from the definition of the iISS property has a very simple form (like an L1 norm). These theoretical results will be useful for our stability analysis of wind turbine systems in Chapter 5. In Chapter 5 we investigate the stability of a variable-speed wind turbine operating under low to medium wind speed. The turbine is controlled to capture as much wind energy as possible. We concentrate on the mechanical level of the turbine system, more precisely on the drive-train with the standard quadratic generator torque controller. We consider both the one-mass and the two-mass models for the drive-train, with the inputs being the deviation of the active torque from an arbitrary positive nominal value and the tracking error of the generator torque. We show that the turbine system is input-to-state stable for the one-mass model and iISS for the two-mass model. Using our abstract results from Chapter 4, we identify the iISS gain of this system. We also propose an adaptive search algorithm for the optimal gain of the quadratic torque controller

A family of asymptotically stable control laws for flexible robots based on a passivity approach

A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility

The converse of the passivity and small-gain theorems for input-output maps

We prove the following converse of the passivity theorem. Consider a causal system given by a sum of a linear time-invariant and a passive linear time-varying input-output map. Then, in order to guarantee stability (in the sense of finite L2-gain) of the feedback interconnection of the system with an arbitrary nonlinear output strictly passive system, the given system must itself be output strictly passive. The proof is based on the S-procedure lossless theorem. We discuss the importance of this result for the control of systems interacting with an output strictly passive, but otherwise completely unknown, environment. Similarly, we prove the necessity of the small-gain condition for closed-loop stability of certain time-varying systems, extending the well-known necessity result in linear robust control.Comment: 15 pages, 3 figure

Energy Conservative Limit Cycle Oscillations

This paper shows how globally attractive limit cycle oscillations can be induced in a system with a nonlinear feedback element. Based on the same principle as the Van der Pol oscillator, the feedback behaves as a negative damping for low velocities but as an ordinary damper for high velocities. This nonlinear damper can be physically implemented with a continuous variable transmission and a spring, storing energy in the spring when the damping is positive and reusing it when the damping is negative. The resulting mechanism has a natural limit cycle oscillation that is energy conservative and can be used for the development of robust, dynamic walking robots

A passivity based control methodology for flexible joint robots with application to a simplified shuttle RMS arm

The main goal is to develop a general theory for the control of flexible robots, including flexible joint robots, flexible link robots, rigid bodies with flexible appendages, etc. As part of the validation, the theory is applied to the control law development for a test example which consists of a three-link arm modeled after the shoulder yaw joint of the space shuttle remote manipulator system (RMS). The performance of the closed loop control system is then compared with the performance of the existing RMS controller to demonstrate the effectiveness of the proposed approach. The theoretical foundation of this new approach to the control of flexible robots is presented and its efficacy is demonstrated through simulation results on the three-link test arm

Integral control of port-Hamiltonian systems: non-passive outputs without coordinate transformation

In this paper we present a method for the addition of integral action to non-passive outputs of a class of port-Hamiltonian systems. The proposed integral controller is a dynamic extension, constructed from the open loop system, such that the closed loop preserves the port-Hamiltonian form. It is shown that the controller is able to reject the effects of both matched and unmatched disturbances, preserving the regulation of the non-passive outputs. Previous solutions to this problem have relied on a change of coordinates whereas the presented solution is developed using the original state vector and, therefore, retains its physical interpretation. In addition, the resulting closed loop dynamics have a natural interpretation as a Control by Interconnection scheme.Comment: 8 pages, 2 figure