Application of the l/sup 1/-optimal regulation strategy to a hard disk servo system

This paper presents the design of an adaptive- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> control algorithm for minimizing the position error signal (PES) in a hard-disk-drive track-following servo. Also, we discuss the results obtained from experiments done on a commercial disk drive using the said scheme. The adaptive- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> control algorithm approach uses the well-known result that all stabilizing controllers for a plant can be synthesized by conveniently parametrized augmentation to a nominal controller. The augmentation to a linear quadratic Gaussian (LQG) optimal control is parametrized by a stable filter <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> . The <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> filter is restricted to a finite-impulse response filter, which minimizes the rms value of the track following error. Experiments done with a fifth-order adaptive filter that uses PES signal as feedback show a 15% improvement in the achievable track misregistration over a model-based LQG controller. The adaptive- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> algorithm implemented via a recursive least squares numerically stable adaptive algorithm shows fast convergence rate and a consistent performance improvement over a fixed controller for various track locations. Also, the tracking performance improves with increase in the adaptive filter order.

Active vibration control systems are commonly reported to be the most robust and effective method for vibration control of structures. However, the type of ground motions and the type of analysis may greatly influence their performances. This study investigates the seismic response of building with and without an active controller under pulse-type ground motions. A 20-story non-linear steel benchmark building is considered. Linear and non-linear analysis is conducted to check the effectiveness of the active control system. Active control with a linear quadratic Gaussian (LQG) control algorithm is applied to the benchmark building for seismic control purposes. Initially, some ground motions are selected following earlier studies from the literature concerning the benchmark building. It is found that the LQG control algorithm is quite effective under the considered earthquakes, and the analysis type does not affect the effectiveness of the controller. Thereafter, a set of additional 69 pulse-type ground motions are considered to check the performance of the LQG control algorithm and to find the suitability of linear analysis. It is noticed that under such pulse-type ground motion, the LQG control algorithm is not much effective if the non-linear behavior of the structure is incorporated in the seismic analysis, whereas in case of linear analysis, the LQG control algorithm is still effective. It is concluded that neglecting the non-linear behavior may lead to unconservative estimates of the seismic response when performing seismic analysis and designing structures equipped with active vibration control systems.

In this study, a frequency-dependent algorithm is proposed in independent modal space as an improvement to the linear quadratic Gaussian (LQG) control algorithm. The passive control parameters such as mass, stiffness and damping of a dynamic system are sensitive to different frequency ratios when subjected to external excitation. Depending upon the sensitivity of these parameters, the algorithm is developed in such a way that a response reduction similar to that of an LQG algorithm can be achieved with a significantly smaller control force. An effective gain is obtained by optimizing the H2 norm of the transfer function. It is observed from the results that the algorithm works well for high frequency ratio and near resonance regimes. Thus, a combination of the LQG and the proposed algorithms is considered as a modified LQG control algorithm, where the effectiveness of both algorithms is utilized. The efficiency of the modified LQG control algorithm is demonstrated by considering a base-isolated structure when subjected to earthquake base excitations. By comparing with the results it is observed that the modified LQG control algorithm is more efficient in terms of response reduction with a much lower control force as compared to the LQG control algorithm. It is envisioned that the modified LQG control algorithm will be highly useful for response control of base-isolated structures.

This paper presents a new design method for submarine depth control. An autopilot strategy based on a noise estimator and an optimal controller is proposed so that the depth keeping of a submersible vehicle at slow speed under a rough sea is improved. A Luenberger observer estimates the disturbances due to the large waves, and this is fed forward into a linear quadratic Gaussian (LQG) optimal control strategy. Simulation results show how the vertical plane movement of the submarine near the surface of a choppy sea is improved.

Using the dual Youla parametrizations of controller based coprime factor plant perturbations and plant based coprime factor controller perturbations, the authors provide a computational procedure for computing an optimal infinite horizon linear quadratic Gaussian (LQG) controller from any stabilizing controller. The method allows the authors to calculate a new optimal LQG controller from a previous one when the plant has slightly changed, and to quantify the change in the controller as a function of the change in the plant. In addition, the authors compute the degradation in the achieved LQG cost when the LQG controller is computed on the basis of a plant model that is "close to" the real plant, where the closeness is measured by some norm of the perturbation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Combined iterative learning and delta-operator adaptive linear quadratic Gaussian control of a commercial rapid thermal processing system

The purpose of this paper is to extend our previous work on the multi-level quantized innovation Kalman filter(MLQ-KF). We consider the linear quadratic Gaussian (LQG) optimal control problem in the discrete systems. Under the assumption that the innovation is approximately Gaussian, it is shown that the separation principle remains valid under the quantized measurement output. The optimal LQG controller is then given in terms of two Riccati difference equations associated respectively with the quantized Kalman filter and the standard LQR control. The corresponding minimum cost is also derived. An illustrative example is included to benchmark our proposed quantized LQG control with the standard LQG control.

Linear quadratic Gaussian (LQG) optimal control systems subject to delayed time-varying and nonlinear perturbations are considered. Some robust stability conditions are derived which result in some bounds on the delayed perturbations so that the systems can remain stable in the sense of uniform ultimate boundedness. The modified Lyapunov equation and the improved Razumikhin-type theory are employed to investigate such robust stability conditions for such a class of LQG optimal control systems. Finally, a numerical example is given to demonstrate the validity of the results.

By modeling the networked robot system (NRS) that drops packets randomly, we considered the problem of optimal linear quadratic Gaussian (LQG) control and analyzed the stability of a NRS. We presented a mathematical model based on a packet-based setting, extended the familiar LQG separation principle that allows us to solve this problem using a standard LQR state-feedback design, proposed an optimal algorithm irrespective of the packet drop pattern by constructing an encoder for the unreliable channel and designing the decoder that uses the information it receives across the link to construct an estimate of the state of the networked robot. For the case of packet drops occurring according to a Markov chain, the stability analysis was carried out. Because the separation theorem for linear systems and quadratic cost does not apply to the general framework of NRSs, we used the uncertainty threshold principle to show that under certain conditions there was a rate for dropped packets for which an undisturbed networked control system with imperfect state observation was mean square stable, used a sub-optimal method to simplify the calculation of the estimator and controller, got the solution to the Riccati-like equation and guaranteed the mean square stability of the NRS with perfect state information. This design does not assume any statistical model of the packet drop events and can be implemented as a small modification of an existing LQG control design

LQG Optimal Control System Design under Delayed Perturbations

Motivated by control applications over lossy packet networks, this paper considers the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when packet losses may occur between the sensors and the estimation-control unit and between the latter and the actuation points. Previous work [1] shows that, for protocols where packets are acknowledged at the receiver (e.g. TCP- like protocols), the separation principle holds. Moreover, in this case the optimal LQG control is a linear function of the estimated state and there exist critical probabilities for the successful delivery of both observation and control packets, below which the optimal controller fails to stabilize the system. The existence of such critical values is determined by providing analytic upper and lower bounds on the cost functional, and stochastically characterizing their convergence properties in the infinite horizon. Finally, it turns out that when there is no feedback on whether a control packet has been delivered or not (e.g. UDP-like protocols), the LQG optimal controller is in general nonlinear, as shown in [2]. There exists a special case, i.e. the observation matrix C is invertible and there is no output noise. In this case this paper shows that the optimal control is linear and critical values for arrival probabilities exist and can be computed analytically.

This paper considers the application of Linear Quadratic Gaussian (LQG) optimal control theory to a problem of cavity locking in quantum optics. Using an equivalence between quantum LQG control and classical LQG control, this problem is reduced to a standard LQG control problem. The cavity locking problem involves controlling the error between the laser frequency and the cavity frequency. A model for the cavity system is set up and an LQG controller is synthesized. The resulting control system implemented on an experimental cavity.

To enlarge the dynamic measurement range and improve the performance by reducing the influence of the main noise including thermo-mechanical noise, 1/f mechanical and tunneling noise, Johnson noise, and shot noise, tunneling sensors usually are operated in a closed-loop mode. Under the assumption that these noises are approximately Gaussian and the tunneling current/gap exponential relationship can be linearized by small-signal linearization, the Linear Quadratic Gaussian (LQG) optimal controller was designed for our micromachined tunneling gyroscope (MTG) to maintain a constant tunneling gap. Simulated results indicated that the distance from the proof mass to the tunneling electrode was effectively regulated to its nominal value of 1 nm thanks to Kalman state estimator associated with the LQG controller. And the closed-control system using LQG control methodology showed an increase of more than 24 dB in signal-noise ratio compared to uncontrolled gyroscope.

We study the problem of salinity regulation in a section of the Mekong Delta in the Tra Vinh district of Vietnam where sluice gates are used to control the sea water flow. An optimal control theoretic method is used to derive a gate closure rate that will minimize the salinity effects and associated costs. We use a linearized version of the shallow water equations and salinity transport equations to represent the system. We derive a linear quadratic Gaussian (LQG) optimal controller for the gate operation. Results are verified via simulations.

This paper discusses the design and testing of two track-following controllers for dual-stage servo systems in hard disk drives. The first controller is designed using the μ-synthesis multivariable robust optimal controller design methodology. The second is designed using classical single-input-single-output (SISO) frequency shaping design techniques, based on sensitivity transfer functions decoupling of the dual-stage actuator. The controllers were implemented and tested on a disk drive with a PZT actuated suspension based dual-stage servo system. The position error signal (PES) for the servo system was obtained by measuring the slider displacement using an LDV and injecting simulated track runout. In the experiment, both designs achieved a track-mis-registration (TMR) less than 10 nm.