Rudolf Sebastian Schittenhelm

Observer design for unbalance excited rotor systems with gyroscopic effect

In state space control, system states are usually estimated using observers. In active rotor systems, observer design often faces two major problems: unbalances acting on the shaft are never known to full extent and in case of a rotor with large discs, gyroscopic effect results in system variation dependent on rotor rotary frequency. Two observer types accounting for these problems, a disturbance observer and an unknown input observer are applied to a rotor system with piezoelectric active bearings. The two approaches are compared with respect to accuracy of the estimated states, transfer behavior and expense for implementation.

Real gyroscopic uncertainties in robust control of flexible rotors

Control laws for flexible high-speed rotors need to account for gyroscopic effects, resulting in a dependency of linear plant models on the rotational speed of the rotor. When these variations are captured by uncertainties in a robust control manner, it is common to employ unstructured or structured complex model perturbations. In order to reduce design-induced conservatism, the synthesis setup presented in this paper deploys a real parametric uncertainty to account for speed-dependent terms of the plant model. The resulting Linear Fractional Transformation (LFT) decomposition of the system can be tackled appropriately using mixed μ synthesis techniques. Suitable approaches for explicit treatment of such problems include (D,G)-K and μ-K algorithms, modifications of the latter being suggested in this paper. To demonstrate potential improvements achievable when using real parametric uncertainties for active vibration control of flexible high-speed rotors via mixed μ synthesis, the methodology is applied with respect to a particular test rig exposed to severe gyroscopic effects. At the hand of this system, efficient performance measures are suggested, leading to promising results both in simulations and validating experiments.

Modal H∞-Control in the Context of a Rotor Being Subject to Unbalance Excitation and Gyroscopic Effect

H∞-optimal controllers are designed for a rotor being subject to unbalance excitation and gyroscopic effect. The system possesses two unbalance-induced resonances within its operating range. The presence of gyroscopic effect is challenging for linear time invariant controller design because of the associated dependence of the system dynamics on the rotational frequency of the rotor. Controllers thus have to be robust against deviation of the actual system behavior from the controller design point model.For vibration control purposes, there are two piezoelectric actuators installed in one of the two supports of the rotor. The signals of four inductive sensors measuring the displacements of the two discs of the rotor are used for controller design.In this article, H∞-optimal controllers are designed on the basis of input and output weighting as well as weighting of modal degrees of freedom and modal excitations. It is shown that superior control performance is achieved using modal weighting since a more accurate problem description of rotors excited by unbalance is incorporated in controller design. Results in this article show furthermore that it is possible to design well performing H∞-optimal controllers for a gyroscopic rotor by means of iterative controller design without taking model uncertainty directly into account via weighting of certain FRFs of the system to be controlled.Copyright

Observer design for rotating shafts excited by unbalance

One of the major problems in controller design for active rotor systems excited by unbalances is the fact that the unbalances acting on the shaft are never known to full extend. If state feedback is applied, this problem reduces to accurate state estimation despite the presence of unbalances. Two observer types accounting for this problem, a disturbance observer and an unknown input observer are applied to a rotor system with piezoelectric active bearings. The two approaches are compared with respect to resulting control performance, accuracy of the estimated states and expense for implementation.

Controllers for Attenuation of Lateral Rotor Vibration Part II: Controller Optimization and Comparison

In part I of this two-part article, three feedback controllers from different fields of research and a feedforward controller have been discussed. In this part II, feedback controllers are optimized to identify the optimum performance which is not necessary for the feedforward controller since it is self-adapting. The four controllers are compared against each other on the basis of their optimal control performance. Results are validated experimentally.

Controllers for Attenuation of Lateral Rotor Vibration Part I: Controller Design

Active Vibration Control has proven to be a good opportunity for attenuation of lateral vibration of rotating shafts in literature. Besides the choice of suitable sensors and actuators, the controller itself has a particularly strong influence on the performance of an Active Vibration Control system since it generates the control signal from sensor signals. There are numerous controller types available for the purpose of active vibration control. These controllers include simple feedback approaches but also more sophisticated model based feedback and feedforward approaches. In this part I of a two-part article three feedback controllers from different fields of research and a feedforward controller are designed for active control of lateral synchronous vibration of a rotor test rig. In particular, PDT1-Control, H∞-Optimal Control, LQG-Control and feedforward control using the FxLMS algorithm are introduced.

Design of Augmented Observer for Rotor Systems

Observers are widely used in state space control and model based fault diagnosis processes. However disturbances and model uncertainties often have large impact on the observation results regarding system states or outputs and result in reduced control or fault diagnosis performances. In rotor systems, observer design often faces two major problems: unbalances acting on the shaft are never known to full extent and in case of a rotor with large discs, gyroscopic effect results in variation of system behavior dependent on rotor rotary frequency. The predominant disturbances e.g. unbalance forces and model uncertainties caused by gyroscopic effect appear in rotor systems in a sinusoidal form with rotor rotary frequency. The influences of unbalance forces and gyroscopic effect can be considered as unknown inputs, and the signals of unknown inputs are also sinusoidal. Augmented observers that account for sinusoidal unknown inputs can be used to take advantage of this characteristic of rotor systems. The augmented observer can be applied in the control or fault diagnosis processes and can be used to estimate the distribution matrix of unknown inputs. According to the design purpose, different configurations of the augmented observer are investigated and their restrictions are discussed in this work. The performance of the augmented observer are presented and discussed with the respect to system states observation as well as fault detection and isolation.

Active damping of aircraft engine shafts using integral force feedback and piezoelectric stack actuators

Unbalance induced vibrations in an aircraft engine shaft are reduced with an active damping system based on piezoelectric stack actuators at the bearing locations. Investigations with a test rig aim at the replacement of squeeze film dampers in aircraft engines with a long-term perspective. In this article controller design using the integral force feedback approach is demonstrated and experimental results achieved from the test rig are presented. The test rig rotor has the characteristics of a 1:2 scaled low pressure shaft of an air-craft engine. For the control system treated in this article, actuator and sensor positions are chosen to be collocated since sensor placement close to the bearings is assumed to be a realistic scenario for an aircraft engine. Such collocated control systems have the advantage of robustness with respect to stability.

Model-Based Fault Detection on a Non-linear Rotor System

This paper describes a model-based fault detection method for nonlinear rotor systems based on a linearised model. The rotational system on which the faults are tested is a non-linear simulation model. The model-based fault detection procedure is developed on the basis of a linearised rotor model, in which the non-linearity is considered as unknown input. In this paper, we consider a rotor system which is supported by means of active bearings with piezoelectric actuators. For simulation purposes, the rotor is modeled with the help of finite element methods based on Timoshenko beam theory. The non-linear behavior of the piezo-actuators are described using the Preisach model. In order to reduce the complexity of the fault detection procedure, this non-linear system has been linearised. The effect of non-linearity is approximated as an unknown input in the linearised model. The linear model with the additional unknown input is intended to deliver the same system output as the non-linear rotor system, and thus can be used for the model-based fault detection and isolation (FDI). The faults which are detected in this paper are point-mass unbalances. The faults are detected on the basis of parity equations and observers. An unknown input observer (UIO) equivalent to parity equations is constructed to separate the disturbances caused due to the unknown inputs on fault detection. The results show that the methods are very effective in detecting the faults in a non-linear system.

Linear Quadratic Regulation of a Rotating Shaft Being Subject to Gyroscopic Effect Using a Genetic Optimization Algorithm

A Linear Quadratic Regulator and a Kalman Filter are designed for a rotor test rig being subject to unbalance excitation and gyroscopic effect. Rotor vibration is controlled by means of two piezoelectric stack actuators installed at one of the two supports of the rotor. The presence of gyroscopic effect leads to an undesirable dependence of the system dynamics on rotational frequency of the shaft. As a result, there is a need for high robustness and furthermore, the separation principle does not hold. Due to the latter aspect, controller and observer design become a coupled problem in the case of the rig. In a first step, the number of free design parameters of the controller-observer combination is reduced to a manageable number of 5. Subsequently, these parameters are determined by means of a genetic optimization algorithm on the basis of a Finite Element model of the test rig. It is shown, that it is possible in this way to determine a controller-observer combination leading to robust stability and excellent performance in the whole operating range which contains two unbalance induced resonances. Control performance is validated in simulation as well as experiments at the test rig.