A Study of Active Rotor-Blade Vibration Control Using Electro-Magnetic Actuation: Part 1 — Theory

Abstract

This is the first paper in a two-part study on active rotor-blade vibration control using electro-magnetic actuation. Emphasis is focused on theoretical aspects of implementing active control into coupled rotor-blade systems, more precisely, into systems where rotor lateral motion is coupled to blades flexible motion. The theoretical investigation includes controllability and observability analyses of such a system in order to determine optimal actuator and sensor placement. An analysis methodology based on modal analysis in time-variant systems, due to the periodic time-variant nature of this kind of system, is presented. The method takes into account the strong vibration coupling which has a significant effect on the controllability and observability of bladed rotor systems. The analyses show that, for tuned bladed rotors, actuators will have to be located within the blades in order to make all vibration modes controllable. However, if the system is deliberately mistuned, rotor and blade vibrations can be controlled using shaft-based actuation and sensing only. Moreover, a controller design procedure for obtaining active periodic time-variant modal controllers, capable to cope with the time-periodicity of the system, is presented. Controllers are designed for a tuned as well as a deliberately mistuned system. The tuned system is controlled using both blade and shaft actuators while the mistuned system is controlled using only shaft actuation. Numerical simulations are provided to show the efficiency of the designed controllers.

Control of Rotor-Blade Coupled Vibrations Using Shaft-Based Actuation

“…In this framework the present paper is a natural continuation of the research works [20,21]. This paper is though devoted to vertical bladed rotors in which the periodic excitation due to gravity and blade weights does not play a significant role.…”

“…A methodology for studying the modal controllability and observability of a bladed disk, considering the rotor and blade vibration coupling, was presented in [19] and a tuned bladed disk was numerically analysed. Active control of a mistuned bladed rotor via shaft-based actuation was studied theoretically as well as experimentally in [20,21]. In those references the dynamic behavior of horizontal bladed rotors was focused, for example, wind turbines with heavy blades.…”

“…These systems are subject to a significant period excitation due to gravity effect and blade weights, which may result in control problems. One of the experimental problems stated in [20,21] was the reduction of control performance because considerable amount of the controller energy had to be used to deal with such periodic excitation. In this case more powerful actuators are needed to suppress parametric vibrations.…”

“…In this case more powerful actuators are needed to suppress parametric vibrations. Furthermore, no analyses of controllability and observability were carried out in [20,21], and such analyses turn out to be of fundamental importance. Due to the presence of the blade stiffening effect, which leads to changes of blade natural frequencies, and interaction among basic and parametric vibration modes, the controllability and observability are, in fact, strongly dependent on angular velocity.…”

“…The main experimental contribution is: v) the verification of control performance improvement, when the controllers do not have to use their energy to deal with the periodic excitation due to the gravity and the blade weights. In other words, the feasibility of controlling blade vibrations in a vertical bladed rotors by means of shaft-based active control is tested, achieving significant better performances than those delivered by the controllers presented in [20,21]. Figure 1(a) shows a schematic drawing of the considered actively controlled coupled rotor-blade system.…”