Adaptive Linear Quadratic Gaussian Control Research Articles

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

Rapid thermal processing (RTP) units are used for various semiconductor fabrication steps mainly due to the short processing time, which results in a low thermal budget and improved product quality. In this study, we propose a comprehensive control system for the RTP unit by combining a linear quadratic Gaussian (LQG) controller, a constrained iterative learning controller (ILC), and a model parameter estimator. The control system is developed to resolve the issues caused by a short sampling time, which is required to meet the refractory control objectives of the modern RTP system (e.g., rapid ramping and a high degree of temperature uniformity). LQG control is selected because most required computations are conducted offline prior to each run and only minor computations are conducted in real time. The LQG control is constructed in a Smith predictor configuration so that a delayed model can be easily incorporated. The LQG control algorithm is modified from the standard formulation to include a quadratic penalty term for input deviation from the average value, to restrain the inputs from violating their constraints in real-time operation. The control algorithm and process model are developed in delta form so that the effect of the truncation error on the model accuracy can be alleviated at a high sampling rate. The constrained ILC updates the feedforward signal of the LQG controller in a batch-wise manner to further increase the temperature uniformity and to ensure that the inputs satisfy their constraints. To overcome model discrepancy from an actual system (patterned wafer), a small number of tunable parameters that can modify the major characteristics of the process model are incorporated into the identified state-space model (bare wafer) and are updated by a model parameter estimator. The performance of the proposed control system is validated in a numerical process, which is precisely constructed through identification experiments in a commercial 12-inch RTP unit.

Adaptive Semiactive Cable Vibration Control: A Frequency Domain Perspective

An adaptive solution to semiactive control of cable vibration is formulated by extending the linear quadratic Gaussian (LQG) control from time domain to frequency domain. Frequency shaping is introduced via the frequency dependent weights in the cost function to address the control effectiveness and robustness. The Hilbert-Huang transform (HHT) technique is further synthesized for online tuning of the controller gain adaptively to track the cable vibration evolution, which also obviates the iterative optimal gain selection for the trade-off between control performance and energy in the conventional time domain LQG (T-LQG) control. The developed adaptive frequency-shaped LQG (AF-LQG) control is realized by collocated self-sensing magnetorheological (MR) dampers considering the nonlinear damper dynamics for force tracking control. Performance of the AF-LQG control is numerically validated on a bridge cable transversely attached with a self-sensing MR damper. The results demonstrate the adaptivity in gain tuning of the AF-LQG control to target for the dominant cable mode for vibration energy dissipation, as well as its enhanced control efficacy over the optimal passive MR damping control and the T-LQG control for different excitation modes and damper locations.

Adaptive control of continuous time stochastic systems

AbstractSome problems and solutions of adaptive control problems for continuous time stochastic systems are described. A solution is given to the adaptive linear quadratic Gaussian control problem under the natural assumptions of controllability and observability. The effects of sampling and numerical differentiation on a least‐squares estimation algorithm are described. Adaptive control problems for non‐linear stochastic systems and linear stochastic distributed parameter systems are briefly described. Copyright © 2002 John Wiley & Sons, Ltd.

Adaptive LQG Control of Input-Output Systems---A Cost-biased Approach

In this paper, we consider linear systems in input-output form and introduce a new adaptive linear quadratic Gaussian (LQG) control scheme which is shown to be self-optimizing. The identification algorithm incorporates a cost-biasing term, which favors the parameters with smaller LQG optimal cost and a second term that aims at moderating the time-variability of the estimate. The corresponding closed-loop scheme is proven to be stable and to achieve an asymptotic LQG cost equal to the one obtained under complete knowledge of the true system (self-optimization). The results of this paper extend in a nontrivial way previous results established along the cost-biased approach in other settings.

Adaptive continuous-time linear quadratic Gaussian control

The adaptive linear quadratic Gaussian control problem, where the linear transformation of the state A and the linear transformation of the control B are unknown, is solved assuming only that (A, B) is controllable and (A, Q/sub 1//sup 1/2/) is observable, where Q/sub 1/ determines the quadratic form for the state in the integrand of the cost functional. A weighted least squares algorithm is modified by using a random regularization to ensure that the family of estimated models is uniformly controllable and observable. A diminishing excitation is used with the adaptive control to ensure that the family of estimates is strongly consistent. A lagged certainty equivalence control using this family of estimates is shown to be self-optimizing for an ergodic, quadratic cost functional.

Adaptive Linear Quadratic Gaussian Control: The Cost-Biased Approach Revisited

In adaptive control, a standard approach is to resort to the so-called certainty equivalence principle which consists of generating some standard parameter estimate and then using it in the control law as if it were the true parameter. As a consequence of this philosophy, the estimation problem is decoupled from the control problem and this substantially simplifies the corresponding adaptive control scheme. On the other hand, the complete absence of dual properties makes certainty equivalent controllers run into an identifiability problem which generally leads to a strictly suboptimal performance. In this paper, we introduce a cost-biased parameter estimator to overcome this difficulty. This estimator is applied to a linear quadratic Gaussian controller. The corresponding adaptive scheme is proven to be stable and optimal when the unknown system parameter lies in an infinite, yet compact, parameter set.

An enhanced LQ adaptive VAr unit controller for power system damping

Static VAR compensators have been installed in power systems primarily to function in the steady state regulation of voltage levels or reactive power flows. More recently however there has been much interest in utilizing these devices to improve the dynamic performance of power systems. This paper presents an adaptive linear quadratic Gaussian control strategy for static var systems to enhance power system damping and stability. The control strategy uses only local information to dampen oscillatory modes present in the network. The controller calculates an appropriate value of VAr unit susceptance to present to the network at each sampling instant. The calculation of the appropriate susceptance value is based on a reduced-order model of the power system which is obtained on-line by a least squares identification procedure. The controller consists of three main components: an identifier, an adaptive observer, adn an adaptive LQG regulator. The identifier users a recursive least squares type of algorithm to fit a linear, discrete transfer function model to a sequence of input and output signals obtained from the power system. This results in a reduced-order approximation to the actual power system. For this study, VAr unit susceptance is used as the input signal and bus frequency deviation is used as the output signal. The coefficients of the identified transfer function are then sent to both the adaptive observer and the adaptive regulator. The observer is an observable-cannonical representation of the system and it calculates a state vector representing system dynamics.

An Enhanced LQ Adaptive VAR Unit Controller for Power System Damping

Static VAR compensators have been installed in power systems primarily to function in the steady state regulation of voltage levels or reactive power flows. More recently however there has been much interest in utilizing these devices to improve the dynamic performance of power systems. This paper presents an adaptive linear quadratic Gaussian control strategy for static var systems to enhance power system damping and stability. The control strategy uses only local information to dampen oscillatory modes present in the network. The controller calculates an appropriate value of VAr unit susceptance to present to the network at each sampling instant. The calculation of the appropriate susceptance value is based on a reduced-order model of the power system which is obtained on-line by a least squares identification procedure. The controller consists of three main components: an identifier, an adaptive observer, adn an adaptive LQG regulator. The identifier users a recursive least squares type of algorithm to fit a linear, discrete transfer function model to a sequence of input and output signals obtained from the power system. This results in a reduced-order approximation to the actual power system. For this study, VAr unit susceptance is used as the input signal and bus frequency deviation is used as the output signal. The coefficients of the identified transfer function are then sent to both the adaptive observer and the adaptive regulator. The observer is an observable-cannonical representation of the system and it calculates a state vector representing system dynamics.