Minimax Linear Quadratic Gaussian Research Articles

A robust control approach for high-speed nanopositioning applications

In this paper, a robust controller for the positioning of a piezoelectric tube scanner (PTS) used in an atomic force microscope (AFM) is proposed. A minimax linear quadratic Gaussian (LQG) controller is designed based on an uncertain system model which is constructed by measuring modeling error between the measured and model frequency response. This controller is robust against uncertainties introduced as a result of spillover dynamics of the scanner at frequencies higher than the first resonance frequency (900 Hz) of the scanner and the variation of plant transfer function due to temperature, humidity, and duration of operation. The proposed controller is applied to the PTS in the AFM used in the experiments to evaluate the performance of the proposed method. It is observed that the proposed scheme provides up to 12 dB closed-loop damping of the resonant mode to track the reference triangular signal. The robust performance of the proposed controller has been investigated for 0–1.96 g sample mass variation. A high positioning accuracy up to 125 Hz frequency is achieved by reducing scanner's vibration and tracking error. Higher-quality imaging up to 125 Hz scanning frequency is achieved compared to the existing PI controller and some other existing methods. This control technique may be applied to control vibration for the systems with changing frequency response due to uncertainties, such as vibration control of disc-drive system.

A Novel Application of Minimax LQG Control Technique for High‐speed Spiral Imaging

AbstractOver the last two decades, increasing the scanning speed of an atomic force microscopy (AFM) has been attempted either by applying novel controllers, using alternative scanning methods, or by modifying the hardware setup. This paper demonstrates, the first two approaches to achieve high‐speed AFM image scanning. A robust minimax linear quadratic Gaussian (LQG) controller is designed and spiral scanning is considered as an alternative scanning method rather than conventional raster scanning. The minimax LQG controller is designed based on an uncertain system model which is constructed by measuring the plant variations due to variations in sample mass and also modeling error between the measured and model frequency responses. This controller is also robust against uncertainties introduced as a result of variations of sample mass, spillover dynamics of the scanner at frequencies higher than the first resonance frequency of the scanner, and variation in plant transfer functions due to temperature and humidity. The designed controller is experimentally implemented on an AFM using a dSPACE ds‐1103 real‐time prototyping system and open‐loop and closed‐loop spiral imaging performances are evaluated. The proposed controller provides sufficient damping at the resonant modes to accurately track the sinusoidal reference signal and generate vibration free images. Also, creep, hysteresis, and cross‐coupling effects are significantly reduced. The experimental results show that the proposed scheme outperforms the open‐loop case and some other existing approaches.

Design of minimax-linear quadratic Gaussian controller using the frequency domain subspace identified model of flexible plate

This paper addresses identification and robust control of vibration of a flexible plate attached to the upper side of an enclosure. The frequency domain subspace methods and minimax-linear quadratic Gaussian (LQG) control are utilized to identify the model and to control the vibration of the flexible plate, respectively. In order to identify the model of the flexible plate, several frequency domain subspace identification algorithms with Instrumental Variable idea are used. Considering the fact that the flexible plate system is stable by nature, all identified unstable models are passed through a stabilized process using an iterative algorithm with different initial values. The first three modes of the plate are selected for control purposes, and the other modes are chosen as uncertainty term. To design the weighting function for the minimax-LQG controller, Chebychev and Yule–Walker filters are utilized to consider the effect of modeling uncertainty. These weights have a great effect on robust stability and performance of the control system. Simulation results are presented to show the effectiveness of the designed controllers for the reference model. Results confirm that some indexes that show the quality of the identified models can be used as suitable measures to predict performance of the designed controller.

Design and Analysis of Robust Minimax LQG Controller for an Experimental Beam Considering Spill-Over Effect

In this brief the design and analysis of an optimal robust minimax linear quadratic Gaussian (LQG) control of vibration of a flexible beam is studied. The analysis is performed by transforming the minimax LQG control design problem to its equivalent mixed sensitivity design problem. The first six modes of the beam in the frequency range of 0-700 Hz are selected for control purpose. Among these modes, three modes in the frequency range of 100-400 Hz are used for control, while the other three modes are left as the uncertainty of modeling. Both the model and the uncertainty are measured based on experimental data. The nominal model is identified from frequency response data and the uncertainty is presented by frequency weighted multiplicative modeling method. For the augmented plant consisting of the nominal model and its accompanied uncertainty, a minimax LQG controller is designed. Analysis and tradeoff between robust stability and robust performance is shown by selecting two different choices of uncertainty modeling. Simulation results used to show how the uncertainty weights can be tuned so that the proposed robust controller increase the damping of the system in its resonance frequencies and maintain the robust stability of the feedback system at the same time.

Voltage mode stabilisation in power systems with dynamic loads

This paper presents a novel modelling and excitation control design to enhance large-disturbance voltage stability in power systems with significant induction motor (IM) loads. The excitation controller is designed using minimax linear quadratic Gaussian (LQG) controller synthesis method. The nonlinear power system model is reformulated with a linear and a nonlinear term. The nonlinear term is the Cauchy remainder in the Taylor series expansion and its bound is used, in this paper, in a robust control design. An advantage of this approach over the existing linearisation scheme is the treatment of the nonlinear dynamic load model in a rigorous framework for excitation control design. The performance of the designed controller is demonstrated by large disturbance simulations on a benchmark power system for various types of loads.

Multivariable Control of Noise in an Acoustic Duct

The paper presents a methodology for designing a multi-input, multi-output active noise control system for an acoustic duct. The design technique proposed in the paper begins with measured frequency response data for the duct from which a state space model is constructed using the subspace approach to system identification. Errors between the measured data and the model are taken into account in constructing an uncertain system model for the duct. Then the minimax linear quadratic Gaussian (LQG) control approach is used to synthesize a controller which minimizes the duct noise level at a specified location in the duct. This controller is robust against uncertainties introduced by neglecting the higher order modes of the duct.

Minimax optimal control of stochastic uncertain systems with relative entropy constraints

This paper considers a new class of discrete time stochastic uncertain systems in which the uncertainty is described by a constraint on the relative entropy between a nominal noise distribution and the perturbed noise distribution. This uncertainty description is a natural extension to the case of stochastic uncertain systems, of the sum quadratic constraint uncertainty description. This paper solves problems of worst-case robust performance analysis and output feedback minimax optimal controller synthesis in a general nonlinear setting. Specializing these results to the linear case leads to a minimax linear quadratic Gaussian (LQG) optimal controller. This controller is defined by Riccati difference equations and a Kalman filter-like state equation. The paper also shows that the minimax LQG problem will have a solution if and only if a corresponding H/sup /spl infin// control problem has a solution. A linear example is presented to illustrate the minimax LQG methodology.