Se Young Yoon

An LMI approach to the control of exponentially unstable systems with input time delay

The stabilization of exponentially unstable linear systems with time-varying input delay is revisited in this paper. The proposed stabilizing controller for input delayed systems with poles in the open right-half plane is obtained from the iterative solution to two LMI problems. First, the upper bound of the delay function is considered to be a known parameter, and a stabilizing controller is found from the feasible solution of an iterative LMI problem. Second, the stabilizing controller is obtained from the optimal solution to an iterative LMI problem, such that the upper bound of the delay function is maximized. The effectiveness of the proposed methods is demonstrated through numerical examples, and by experimental testing on a balanced beam test rig.

Experimental Evaluation of a Surge Controller for an AMB Supported Compressor in the Presence of Piping Acoustics

This brief studies the active control of compressor surge using the thrust active magnetic bearing (AMB) in centrifugal compressors and it presents experimental test data to demonstrate the effectiveness of the control solution in industrial size equipment. A detailed step-by-step description is provided from the derivation of the surge model, to the implementation and experimental testing of the surge controller. To accurately represent the configurations found in industrial systems, the proposed surge suppression method is implemented integrally using common off-the-shelf components. During the design of the surge controller, special attention is paid to a possible conflict between the surge controller and the AMBs internal rotor levitation controller. Observations from the experimental surge testing demonstrate that the presented method is able to stabilize the compression system when operating in the unstable surge region, extending the stable flow range by over 21%. In practice, this allows the compressor to operate at the peak pressure/efficiency point, while maintaining a healthy surge margin as commonly prescribed in industrial compressors.

Coordinated Control of Wheeled Vehicles in the Presence of a Large Communication Delay Through a Potential Functional Approach

This paper studies the flocking problem for a multiagent system, where each agent is a vehicle with nonholonomic dynamics. In particular, we consider the case where the agents are subjected to an arbitrarily large communication delay. A distributed low gain control law is derived based on the gradient of an artificial potential function. We demonstrate using the Lyapunov functional approach that the proposed control law drives the multiagent system into the stable flocking behavior. The effectiveness of the proposed control law is verified in numerical simulation.

Control of compressor surge with Active Magnetic Bearings

The design of an active surge controller, which employs Active Magnetic Bearings (AMBs) to stabilize the flow in the compressor, is presented in this paper. The axial tip clearance of an unshrouded centrifugal impeller from a single stage compressor is modulated relative to the static shroud to induce a pressure variation in the compressor output pressure. This fast-response, high-precision control of the output pressure is employed to stabilize the compressor operating in surge condition. The control law for the tip clearance is derived based on a recently introduced mathematical model, and the performance of the controller is tested through simulation.

Model Validation for an Active Magnetic Bearing Based Compressor Surge Control Test Rig

In this paper, we present experimental test data for the validation of a recently introduced mathematical model for centrifugal compression systems with variable impeller axial clearances. Employing the active magnetic bearings (AMBs) of a compressor built for the experimental study of surge, the axial clearance between the impeller and the static shroud is servo controlled, and the measured variations in the compressor output flow are compared with the mathematical model. The steady state and the dynamic responses of the compression system induced by varying the impeller tip clearance are measured and compared with the theoretical predictions, and the states of the compression system in surge condition are collected and analyzed. Parameters in the compression system model, such as the Greitzer parameter B and Helmholtz frequency ω H are experimentally identified. Also, the servo dynamics of the magnetic bearing that controls the axial impeller position is determined experimentally. To further validate the mathematical model and the feasibility of using the impeller tip clearance for controlling surge, we present a design example for an active surge controller based on the derived model, and simulate the response of the compression system. This design exercise also helps us understand the possible challenges that one could face in the design and implementation of a successful surge controller.

Predictor based control of linear systems with state, input and output delays

In this paper we develop a predictor-based controller for linear systems with state, input and output delays. First, a state predictor is developed for state feedback control. This predictor is formulated recursively over the prediction time by partitioning the input delay into sections smaller than the state delays. The partitioning of the input delay ensures that the resulting predictor equation only depends on the past values of the state and input. It is shown that the proposed predictor gives an exact prediction of the future states. This recursive predictor is then reformulated into a cascade form in order to reduce the number of redundant calculations and to simplify the predictor equation for practical implementation. We construct a predictor based state feedback control law and show that the spectrum of the closed-loop time-delay system under the constructed control law is the same as that of an equivalent time-delay system without input delay and under the nominal state feedback control. Therefore, the proposed predictor based solution can stabilize the delay system if a stabilizing state feedback control law exists for the input delay free system. These state feedback results are then extended to the case of delayed output feedback. The theoretical derivation is verified through numerical examples.

Introduction to Rotor Dynamics

Rotor-dynamics studies the lateral and torsional vibrations of rotating shafts, with the objectives of predicting the rotor vibrations and constraining the vibration level under an acceptable limit. In this chapter we present a short introduction to rotor dynamics to familiarize the reader with the basic concepts and terminologies commonly used in describing rotor/AMB systems. First, the mathematics behind the basic rotor-dynamic principles are derived by introducing a simple rotor/bearing system known as the Foppl/Jeffcott rotor. The primary concerns in rotor-dynamic systems, including the critical speed, unbalance response, gyroscopic effects and instability excitation, are discussed in this chapter. Finally, the American Petroleum Institute (API) standards for auditing the rotor response in compressors are presented. Most of these standards are directly applicable to compressors with AMBs, and they play an important role in the design of the AMB levitation controllers.

Model validation for an AMB-based compressor surge control test rig

In this paper, we present experimental test data for validation of a recently introduced mathematical model for compression systems, including the dynamic effects of varying the impeller axial tip clearance. For the centrifugal compressor test rig that was built to study the suppression of surge by using active magnetic bearings (AMBs) to control its impeller tip clearance, the steady state and the dynamic response of the compression system induced by varying the impeller tip clearance are measured and compared to theoretical predictions, and the states of the compression system in surge condition are collected and analyzed. Parameters in the compression system model, such as the Greitzer parameter B and Helmholtz frequency ωн are experimentally identified. Also, the servo dynamics of the magnetic bearing that controls the axial impeller position is determined experimentally.

Modal Tilt/Translate Control and Stability of a Rigid Rotor with Gyroscopics on Active Magnetic Bearings

Most industrial rotors supported in active magnetic bearings (AMBs) are operated well below the first bending critical speed. Also, they are usually controlled using proportional, integral and derivative controllers, which are set up as modally uncoupled parallel and tilt rotor axes. Gyroscopic effects create mode splitting and a speed-dependent plant. Two AMBs with four axes of control must simultaneously control and stabilize the rotor/AMB system. Various analyses have been published considering this problem for different rotor/AMB configurations. There has not been a fully dimensionless analysis of these rigid rotor AMB systems. This paper will perform this analysis with a modal PD controller in terms of translation mode and tilt mode dimensionless eigenvalues and eigenvectors. The number of independent system parameters is significantly reduced. Dimensionless PD controller gains, the ratio of rotor polar to transverse moments of inertia and a dimensionless speed ratio are used to evaluate a fully general system stability rigid rotor analysis. An objective of this work is to quantify the effects of gyroscopics on rigid rotor AMB systems. These gyroscopic forces reduce the system stability margin. The paper is also intended to help provide a common framework for communication between rotating machinery designers and controls engineers

An enhanced Greitzer compressor model with pipeline dynamics included

The modeling of a centrifugal compressor system with exhaust piping acoustics is presented in this paper. For a centrifugal compressor test rig with modular inlet and exhaust piping, a mathematical model is derived based on the Greitzer compression system model. In order to include the dynamics of the piping acoustics, a transmission line model is added to the original compressor equations, and different compressor piping configurations are tested. The simulation of the resulting mathematical models of the compression system are compared to the measured response. Employing active magnetic bearings to perturb the axial impeller tip clearance of the compressor, the compression system is excited over a wide frequency range and the input-output response from the impeller disturbance to the plenum pressure rise is analyzed. A good agreement is observed between the experimental and theoretical Bode plots.