Ravinder Venugopal

Modeling, identification, and feedback control of noise in an acoustic duct

Although active noise control has been a subject of interest for over 50 years, it has become feasible only with recent technological advances. This paper formulates the problem of noise control in a one-dimensional acoustic duct in a form that lends itself to the application of feedback control theory. In contrast to most of the literature on the subject which uses feedforward techniques, a feedback approach is used. Inconsistencies that appear in previous feedback control models are rectified, controllers are designed using precompensated linear quadratic Gaussian (LQG) synthesis, and experimental verification of the control designs is presented. The experimental results show a reduction of about 5-12 dB over a frequency range from 150-350 Hz.

Adaptive disturbance rejection using ARMARKOV system representations

An adaptive disturbance rejection algorithm is developed for the standard control problem. The MIMO system and controller are represented as ARMARKOV/Toeplitz models, and the parameter matrix of the compensator is updated online by means of a gradient algorithm. The algorithm requires minimal knowledge of the plant, specifically, the numerator of the ARMARKOV transfer function from control to performance is required. No knowledge about the spectrum of the disturbance is needed. Experimental results demonstrating tonal and broadband disturbance rejection in an acoustic duct are presented.

Adaptive disturbance rejection using AR-MARKOV/Toeplitz models

We develop an adaptive disturbance rejection algorithm formulated in terms of an AR-MARKOV/Toeplitz matrix system representation. The algorithm is applied to the problem of active noise suppression in an acoustic duct, and experimental results demonstrating tonal and broadband disturbance rejection are presented.

State space modeling and active control of slosh

The wave motion of fluids in finite containers, called slosh, is known to have adverse effects on the dynamics of aerospace vehicles and tanker trucks as well as on large storage tanks during earthquakes. This paper investigates slosh from an active feedback control perspective, and considers two possible active control methods for attenuating the response of the fluid to an external disturbance acceleration acting on the tank. The first method uses surface pressure control, whereas the second method uses a flap actuator on the surface of the fluid. In the first part of the paper we derive a state space model of slosh in a tank of rectangular cross section. This model is then used to design feedback controllers using LQG synthesis, and simulation results are presented to demonstrate the closed-loop performance.

Logarithmic Lyapunov functions for direct adaptive stabilization with normalized adaptive laws

The problem of discrete-time and continuous-time adaptive stabilization under full-state feedback control is considered. In the discrete-time case the main result is based on a gain update law involving a step-size function. The formulation generalizes and unifies prior results based on quadratic and logarithmic Lyapunov functions. In the continuous-time case adaptive stabilization under full-state feedback using a normalized gradient algorithm is considered and Lyapunov stability is demonstrated.

Optimal Lyapunov-based backward horizon adaptive stabilization

We derive a discrete-time adaptive stabilization algorithm and prove closed-loop attractivity with respect to the plant states. In this paper, we use a new method of analysis based on a modified Lyapunov technique and an adaptive step size. We begin by considering a one-step backward-horizon cost function, whose gradient provides an update direction for modifying the feedback gain matrix. The step size in the gradient direction is chosen to minimize the cost function along that direction. Finally, we use a modified Lyapunov technique to prove convergence of the plant states to the origin. We present the main results of Goodwin et al. (1980). An unstable and abruptly varying plant was simulated. Implementation issues are discussed and some results from simulation studies are presented.

State Space Modeling of an Acoustic Duct With an End-Mounted Speaker

This paper develops a state space model of the dynamics of an acoustic duct with end-mounted speakers. The initial model formulation includes the forcing term as part of the boundary conditions. The shifted particle velocity is then defined to transform the nonhomogeneous boundary conditions into homogeneous boundary conditions and thus develop the state space model. It is shown that the speaker and acoustic dynamics interact by means of feedback in which the speaker creates an acoustic field, which, in turn, affects the motion of the speaker cone. This interaction is studied using positive real closed-loop feedback analysis, and shifts in the modal frequencies of the duct due to the presence of the end-mounted speaker are predicted.

Adaptive control of a flexible membrane using acoustic excitation and optical sensing

Flexible membranes are envisioned as a key component of large, lightweight, space-based systems. This paper focuses on the problem of adaptive disturbance rejection, that is, the rejection of external disturbances with unknown spectral content. It describes the design and operation of a laboratory testbed involving a exible membrane with acoustic excitation and optical sensing. The ARMARKOV adaptive disturbance rejection algorithm is used to reject single- and dual-tone disturbances without knowledge of the disturbance spectrum and with limited modeling of the membrane dynamics.

Experimental comparison of adaptive cancellation algorithms for active noise control

With the success of adaptive cancellation methods developed largely within the active noise control community, it is of interest to understand these algorithms within a more traditional feedback control framework. This paper thus has two goals, namely, to systematically describe three such algorithms (two LMS algorithms and the recently developed ARMARKOV/Toeplitz algorithm) in standard feedback control terminology, and to experimentally compare the performance of the algorithms. For experimental purposes, we use an acoustic duct testbed with both tonal and broadband disturbances.

Multi-Input Multi-Output (MIMO) Modeling and Control for Stamping

The binder force in sheet metal forming controls the material flow into the die cavity. Maintaining precise material flow characteristics is crucial for producing a high-quality stamped part. Process control can be used to adjust the binder force based on tracking of a reference punch force trajectory to improve part quality and consistency. The purpose of this paper is to present a systematic approach to the design and implementation of a suitable multi-input multi-output (MIMO) process controller. An appropriate process model structure for the purpose of controller design for the sheet metal forming process is presented and the parameter estimation for this model is accomplished using system identification methods. This paper is based on original experiments performed with a new variable blank holder force (or variable binder force) system that includes 12 hydraulic actuators to control the binder force. Experimental results from a complex-geometry part show that the MIMO process controller designed through simulation is effective.