Stability of closed-loop fractional-order systems and definition of damping contours for the design of controllers

Fractional complex order integrator has been used since 1991 for the design of robust control-systems. In the CRONE control methodology, it permits the parameterization of open loop transfer function which is optimized in a robustness context. Sets of fractional order integrators that lead to a given damping factor have also been used to build iso-damping contours on the Nichols plane. These iso-damping contours can also be used to optimize the third CRONE generation open-loop transfer function. However, these contours have been built using non band-limited integrators, even if such integrators reveal to lead to unstable closed loop systems. One objective of this paper is to show how the band-limitation modifies the left half-plane dominant poles of the closed loop system and removes the right half-plane ones. It is also presented how to obtain a fractional order open loop transfer function with a high phase slope and a useful frequency response. It is presented how the damping contours can be used to design robust controllers, not only CRONE controllers but also PD and QFT controllers

Unified control/structure design and modeling research

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed

A Unified Framework for the Study of Anti-Windup Designs

We present a unified framework for the study of linear time-invariant (LTI) systems subject to control input nonlinearities. The framework is based on the following two-step design paradigm: "Design the linear controller ignoring control input nonlinearities and then add anti-windup bumpless transfer (AWBT) compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance". The resulting AWBT compensation is applicable to multivariable controllers of arbitrary structure and order. All known LTI anti-windup and/or bumpless transfer compensation schemes are shown to be special cases of this framework. It is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model. The actual analysis of stability and performance, and robustness issues are problems in their own right and hence not detailed here. The main result is the unification of existing schemes for AWBT compensation under a general framework

Robust Scale-Free Synthesis for Frequency Control in Power Systems

The AC frequency in electrical power systems is conventionally regulated by synchronous machines. The gradual replacement of these machines by asynchronous renewable-based generation, which provides little or no frequency control, increases system uncertainty and the risk of instability. This imposes hard limits on the proportion of renewables that can be integrated into the system. In this paper we address this issue by developing a framework for performing frequency control in power systems with arbitrary mixes of conventional and renewable generation. Our approach is based on a robust stability criterion that can be used to guarantee the stability of a full power system model on the basis of a set of decentralised tests, one for each component in the system. It can be applied even when using detailed heterogeneous component models, and can be verified using several standard frequency response, state-space, and circuit theoretic analysis tools. Furthermore the stability guarantees hold independently of the operating point, and remain valid even as components are added to and removed from the grid. By designing decentralised controllers for individual components to meet these decentralised tests, every component can contribute to the regulation of the system frequency in a simple and provable manner. Notably, our framework certifies the stability of several existing (non-passive) power system control schemes and models, and allows for the study of robustness with respect to delays.Comment: 10 pages, submitte

Generalizing Negative Imaginary Systems Theory to Include Free Body Dynamics: Control of Highly Resonant Structures with Free Body Motion

Negative imaginary (NI) systems play an important role in the robust control of highly resonant flexible structures. In this paper, a generalized NI system framework is presented. A new NI system definition is given, which allows for flexible structure systems with colocated force actuators and position sensors, and with free body motion. This definition extends the existing definitions of NI systems. Also, necessary and sufficient conditions are provided for the stability of positive feedback control systems where the plant is NI according to the new definition and the controller is strictly negative imaginary. The stability conditions in this paper are given purely in terms of properties of the plant and controller transfer function matrices, although the proofs rely on state space techniques. Furthermore, the stability conditions given are independent of the plant and controller system order. As an application of these results, a case study involving the control of a flexible robotic arm with a piezo-electric actuator and sensor is presented

Stability analysis and \mu-synthesis control of brake systems

The concept of friction-induced brake vibrations, commonly known as judder, is investigated. Judder vibration is based on the class of geometrically induced or kinematic constraint instability. After presenting the modal coupling mechanism and the associated dynamic model, a stability analysis as well as a sensitivity analysis have been conducted in order to identify physical parameters for a brake design avoiding friction-induced judder instability. Next, in order to reduce the size of the instability regions in relation to possible system parameter combinations, robust stability via \mu-synthesis is applied. By comparing the unstable regions between the initial and controlled brake system, some general indications emerge and it appears that robust stability via \mu-synthesis has some effect on the instability of the brake system