S. M. Yang

Design of Experiments for the Controller of Rotor Systems With a Magnetic Bearing

A new design methodology for the vibration control of rotor systems with a magnetic bearing is developed in this paper. The methodology combines the experimental design method in quality control engineering and the conventional PD control technique such that their advantages in implementation feasibility and performance-robustness can be integrated together. A quality loss index defined by the summation of the infinity norm of unbalanced vibration is used to characterize the system dynamics. By using the location of the magnetic bearing and PD feedback gains as design parameters, the controller can be determined by a small number ofmatrix experiments to achieve the best system performance. In addition, it is robust to the vibration modes within a desired speed range. A rotor system consisting of rigid disks, 3 isotropic bearings, and l magnetic bearing is applied to illustrate the feasibility and effectiveness of the experiment-aided controller design.

Simulating Displacement and Velocity Signals by Piezoelectric Sensor in Vibration Control Applications

Intelligent structures with built-in piezoelectric sensor and actuator that can actively change their physical geometry and/or properties have been known preferable in vibration control. However, it is often arguable to determine if measurement of piezoelectric sensor is strain rate, displacement, or velocity signal. This paper presents a neural sensor design to simulate the sensor dynamics. An artificial neural network with error backpropagation algorithm is developed such that the embedded and attached piezoelectric sensor can faithfully measure the displacement and velocity without any signal conditioning circuitry. Experimental verification shows that the neural sensor is effective to vibration suppression of a smart structure by embedded sensor/actuator and a building structure by surface-attached piezoelectric sensor and active mass damper.

Vibration Control of Rotor Systems With Noncollocated Sensor/Actuator by Experimental Design

This paper presents a controller design methodology for vibration suppression of rotor systems in noncollocated sensor/actuator configuration. The methodology combines the experimental design method of quality engineering and the active damping control technique such that their advantages in implementation feasibility and performance-robustness can be integrated together. By using the locations of sensor/actuator and the feedback gains as design parameters, the controller design is shown to achieve a near optimal performance within the two-sigma confidence among all possible parameter combinations. Compared with LQ-based designs, the controller order is smaller and it is applicable to systems in an operation speed range. In addition, neither preselected sensor/actuator location(s) nor state measurement/ estimation is needed.

Analytical Solution of Whirl Speed and Mode Shape for Rotating Shafts

The analytical solution of whirl speed and mode shape of a rotating shaft in six boundary conditions is presented in this paper. The shaft is modelled by a Rayleigh beam with rotatory inertia and gyroscopic effects, and the boundary conditions are (1) short-short, (2) long-long, (3) long-free, (4) free-free, (5) long-short, and (6) short-free bearings. It is shown that the whirl speed can be written analytically by a function of the whirl ratio (λ) defined by the rotating speed over the whirl speed and the slenderness ratio (l) defined by the length of the shaft over its radius. The number of whirl speeds, contrary to common belief, is finite when λ > 1/2. For the first time, the rotating system’s unbalanced response can be written analytically in an exact form by a finite number of vibration modes with the corresponding generalized coordinates.Copyright

Experiment-Aided Controller Design of Rotor Systems With a Magnetic Bearing

A new design methodology for the vibration control of rotor systems with a magnetic bearing is developed in this paper. The methodology combines the experimental design method in quality control engineering and the conventional PD control technique such that their advantages in implementation feasibility and performance-robustness can be integrated together. A quality loss index defined by the summation of the infinity norm of unbalanced vibration is used to characterize the system dynamics. By using the location of the magnetic bearing and PD feedback gains as design parameters, the controller of experiment-aided design achieves the best system performance. In addition, it is robust to operating speed variations. A rotor system consisting of 4 rigid disks, 3 isotropic bearings, and 1 magnetic bearing is applied to illustrate the feasibility and effectiveness of the experiment-aided controller design.© 1995 ASME

The Use of Routh Array for Testing the Hurwitz Property of a Segment of Polynomials

Abstract In this paper we show that the Hurwitz property of a segment of polynomials (1 – λ) p 0 (s) + λ p 1 (s), where λ ∈ [0,1], p 0 (s) and p 1 (s) are nth-degree polynomials of real coefficients, can be tested via constructing a fraction-free Routh array and using Sturm’s theorem. As a result, the robust Hurwitz stability of a convex combination of polynomials can be checked in a finite number of arithmetic operations without having to invoking any root-finding procedure.

Plant Template Generation for Time-Delay Systems in Quantitative Feedback Control Theory

Abstract In this paper we present a necessary and sufficient condition for the zero inclusion of the value set f ( T , Q ) = f ( τ , q ) : τ ϵ T : = τ − , τ + , q ϵ Q : = ∏ k = 0 m − 1 q k − , q k + , where f(τ, q) = g(q) + h(q)e-jτw with g(q) and h(q) being both complex-valued affine functions of the m-dimensional real vector q and ω a fixed frequency. Based on this condition we develop an efficient zero inclusion test algorithm for the value set f(T, Q). This zero inclusion test algorithm is applied along with a pivoting procedure to generate plant templates for a class of linear systems with an uncertain time delay and affine parameter perturbations in coefficients. To illustrate the efficiency of the algorithm, an example is provided.

Optimal Design of Sensor/Actuator Location and Feedback Gain by Taguchi Method

Abstract This paper presents a controller design methodology for optimal of sensor/actuator location and feedback gain. The methodology combines Taguchi method in quality control engineering and classical PID control such that their advantages in implementation feasibility and performance robustness can be integrated together. Instead of searching for all possible combinations of design parameters, a reduced set of experimental design-the orthogonal array in Taguchis method-is applied to search for a near optimal design. Several orders of magnitude in the effort of controller design can thus be reduced. The controller is shown to achieve the best possible system performance while maintaining the closed loop system stability. A rotor system is applied to illustrate the feasibility and effectiveness of the controller.