LQG Control Design Research Articles

The optimal placement of actuator and sensor for active noise control of sound–structureinteraction systems

This paper presents new objective functions and a practical method for finding the optimalplacement of actuator and sensor for a sound–structure interaction system. The developedmethod for optimal actuator and sensor positioning is based on an energy-based approachand model uncertainty. The optimal actuator and sensor location obtained is used toconstruct a feedback controller using a minimax LQG control design method for reducingacoustic potential energy caused by structure-borne sound inside the acoustic cavity. Theexperimental demonstration of the novel method presented in this paper attenuatesstructural vibration up to 17 dB over the entire frequency range of interest and theassociated noise up to 10 dB without explicit knowledge of the acoustic model.

A sequential LQG approach to nonlinear tracking problem

A new approach, named the sequential LQG solution for nonlinear and nonstationary systems tracking problem, has been proposed in the article. Proposed method for tracking of a desired reference trajectory uses a state space model of the multivariable nonlinear/nonstationary system. The method involves three steps. The first step is the design of nominal trajectory using the predictive control technique. The second step is the sequential linearization of the nonlinear system around the fixed operating points, chosen in accordance to the plant dynamics changes. The third step involves the choice of the weighting matrices in the classical LQG controller design for the sequence of linearized models. The feasibility of the proposed method has been demonstrated through its application to the control of aircraft, represented by the six-degree-of-freedom model around the prespecified nominal trajectory.

Optimal LQG control across packet-dropping links

We examine two special cases of the problem of optimal linear quadratic Gaussian control of a system whose state is being measured by sensors that communicate with the controller over packet-dropping links. We pose the problem as an information transmission problem. Using a separation principle, we decompose the problem into a standard LQR state-feedback controller design, along with an optimal encoder–decoder design for propagating and using the information across the unreliable links. Our design is optimal among all causal algorithms for any arbitrary packet-drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design.

A robust LQG-controller design for DPS

We review the popular Linear Gaussian Quadratic (LQG) controller design for DPS and its shortcomings. In particular, its applicability is essentially restricted to exponentially stabilizable and detectable DPS with finite-rank bounded input and output operators. As an alternative, we propose a new practical control design that is applicable to DPS with unbounded, finite-rank input and output operators, provided that the generator has finitely many unstable eigenvalues and satisfies the spectrum determined growth assumption.

Measured linear–quadratic–Gaussian controlled damping

This paper investigates experimentally the characteristics of LQG control for controlledvibration mitigation. The control algorithm is implemented in LabVIEW RT. Thecontroller performance is measured at a test set-up consisting of a vibrating taut cable withMR damper. Measurements of the closed-loop system clearly point out that LQG controlenables damping vibrations with respect to their intensity and frequency. When thecable is excited at constant frequency, the desired control force is dissipativeand proportional to the vibration velocity at the damper position. Thus, for thesystem under consideration, LQG control ends up in the desired viscosity. Withincreasing frequency of the cable excitation, the desired viscosity decreases. Thedesired viscosities for the first four cable modes depend on the pole locationsof the observer and regulator. The nearer they are located, the higher are thedesired viscosities. Therefore, a design parameter describing precisely the distancebetween observer and regulator poles is introduced. Based on this design parameter,the paper proposes a systematic method of LQG controller design for practicalapplications.

Using process tomography as a sensor for optimal control

In this paper, model-based control is discussed when the observations are based on diffuse tomography such as impedance tomography. Diffuse tomography is a notoriously difficult class of inverse ill-posed problems which in the case of control system design means that the computation of the state estimates is basically an unstable problem. Recent results in the field of nonstationary inverse problems have shown that accurate modeling of the state and observation models may facilitate stable state estimation, which in turn would facilitate feedback control. When the state evolution model is based on partial differential equations, the price to pay is that the dimension of the state is invariably very large since state reduction leads to intolerable approximation errors. In this paper, the basic LQG control design based on impedance tomographic measurements is considered when the state is governed by a stochastic convection–diffusion equation. It is shown with simulations that proper stochastic modeling of the state evolution can enable one to obtain such state estimates that facilitate feedback control.

IMPROVING THE TILT CONTROL PERFORMANCE OF HIGH-SPEED RAILWAY VEHICLES: AN LQG APPROACH

The paper discusses on the use of an optimal LQG control design to improve the vehicle curving performance at increased running speed, employing only local (rail vehicle-based) signal measurements. It addresses the fundamental problem related with straightforward feedback control, and introduces the commercially-used command-driven with precedence scheme. A combination of simulation results and, a recently proposed, tilt control system assessment method are utilised for assessing the overall performance of the tilt controller.

MINIMAX LQG CONTROL FOR UNCERTAIN SYSTEMS WITH A NORMALISED COPRIME FACTOR UNCERTAINTY STRUCTURE

The paper extends the recently developed robust LQG control design methodology to stochastic uncertain systems with a normalised coprime factor uncertainty structure. To consider this class of model uncertainties, a special technique of probability measure transformations is developed. As a by-product, other types of the model uncertainty, for example, those reflecting passivity of the uncertainty, are captured.

Adaptive LQG controller tuning

Controller tuning is a basic step in any control application. This tuning is a complex process composed of several steps starting with the plant analysis and ending with the verification of the designed controller. There are various tools that help in particular steps of the design but the complete path of the design is not supported. An attempt is made to offer a procedure of ‘complete’ controller design where all necessary steps follow automatically one after the other. The idea is applied to LQG controller design. The whole procedure is described and demonstrated on an example with the emphasis on the tuning of the LQG criterion to respect given constraints.

Model validation and controller design for vibration suppression of flexible rotor using AMB

This paper discusses the model validation and vibration suppression of an AMB flexible rotor via additional LQG controller. The main difficulty in the vibration suppression of the flexible rotor using AMB is to realize a controller that can minimize resonance without injuring the stabilized rigid modes. In order to solve this problem, simple scheme for system modeling and controller design are developed. Firstly, the AMB flexible rotor is stabilized with a PID controller, which leads to a new stable rotor-bearing system. Then, authors propose the model validation procedure using measured open-loop frequency responses to obtain an accurate model of the AMB flexible rotor system. After that, LQG controller with modal weighting is designed to suppress resonances of the stable rotor-bearing system. Due to the poor controllability and observability of flexible modes compared to rigid ones, balancing of two Gramians is prerequisite for the fair LQG controller design. Simulation with step disturbance and experimental results of unbalance response up to 10,000 rpm verified the effectiveness of the proposed scheme.

Iterative Identification and LQG Control Design for Time Delay Systems

This paper deals with an LQG control problem for input time delay systems using closed-loop identification. A virtual system is introduced to solve a spectral factorization, which does not include integral operator. The solution of the factorization is used as a prefilter of closed-loop identification. An iterative identification and control design method is applied and some numerical examples are shown.

A LQG CONTROLLER DESIGN FOR LINEAR CONTINUOUS-TIME SYSTEMS BASED ON INPUT-OUTPUT DATA

In this paper, a new LQG control design based on input-output data for linear time invariant continuous-time systems is proposed. Considering the laguerre series expansion of input-output signals, the controller can be synthesized using only the coefficients by an algebraic calculation. The analysis of the system transformed by the laguerre series expansion is utilized to lead this design method. Comparing the proposed controller with the model-based one through a numerical simulation, the effectiveness is illustrated.

Reliable LQG control with sensor failures

The paper deals with reliable LQG controller design for linear systems with sensor failures. A model of sensor failures more practical than outage is adopted. Two procedures of designing reliable LQG controllers are presented: stabilising solutions of three coupled Riccati equations; and solutions to one Riccati equation and two linear matrix inequalities. The resulting control systems are guaranteed to be robustly stable and with a known cost bound on the LQG cost against sensor failures. Algorithms are developed to obtain a solution and illustrated via numerical examples.

Self-Tuning SIMO AVR Control with Multi-Variable Identification

A self-tuning polynomial LQG controller design procedure developed for industrial applications in the electrical power sector will be introduced. Special attention is given to the choice of the algorithms needed, to obtain a solution which can be implemented and used in practice. It is shown that for SIMO plants, simplifications can be made which reduce algorithm complexity. The self-tuning LQG controller is demonstrated by a case-study of AVR control.

Robust LQG controller design for lightly damped uncertain linear systems

In this note, we consider lightly damped uncertain linear systems with natural frequency variations. This type of uncertainty has multiple uncertain parameters with multiple rank structure. It is well known that the conventional LQG or LQG/LTR methods can not be applied to such system bccause of the instability and the design conservatism. To overcome such shortcomings, we propose a systematic method to design robust LQG controllers. The proposed method requires only the LQG tuning parameters and the structure information of uncertainty. It will be shown that our approach can be effectively applied to flexible structure control design problems.

Practical Design and Verification of LQG Controllers as Applied to Active Structures

Many mechanical engineers find difficulty in applying LQG controllers to active mechanical structures. Answers to frequently asked questions are provided here, describing in detail the procedure as applied to a ca. 2 m x 0.5 m panel where vibrations are to be actively damped. This application was chosen because of the number of difficulties it can throw light on, while remaining simple enough to be understood with common sense. From another point of view, LQG controllers, as applied to mechanical structures with a theoretical infinity of degrees of freedom, have a bad reputation concerning stability. However, mechanical understanding of the reasons for the behavior helps to find very practical solutions. After reviewing the most important equation sets, a method for designing an LQG-controller is given. It mainly includes the design of the observer filter and the design of a feedback gain matrix considering the ideal knowledge of the system state vector. The test bed and its instrumentation is described. Physical measurements and computations are outlined as well as the integration of both theoretical and practical data into the same procedure aiming to determine system parameters. In the first step, only bending is considered. The experimental behavior shows a spillover due to bending modes not considered. Two methods are proposed in order to suppress this spillover. The first considers the sensor signal given by the uncontrolled dynamics as a noise. The second improves the estimation of the structural state without changing the controller gains. Both have advantages and disadvantages that are outlined. Finally, torsion is included in order to improve the behavior.

From Noise Contaminated Pulse Responses to Design of LQG Controller

Abstract This paper proposes to design a dynamic controller from the measured impulse responses of the plant without constructing its parametric model like state space representation. We call the proposed method the response-based design method. Using the estimated impulse response of the system and the auto correlation matrices of the responses due to system and measurement noises, which are identified from the noise contaminated impulse responses, the LQG dynamic controller is designed. Some numerical results that validate the efficiency of the method is also presented.

Probability‐one homotopy algorithms for full- and reduced‐order H2/H controller synthesis

Homotopy algorithms for both full- and reduced-order LQG controller design problems with an H∞ constraint on disturbance attenuation are developed. The H∞ constraint is enforced by replacing the covariance Lyapunov equation by a Riccati equation whose solution gives an upper bound on H2 performance. The numerical algorithm, based on homotopy theory, solves the necessary conditions for a minimum of the upper bound on H2 performance. The algorithms are based on two minimal parameter formulations: Ly, Bryson and Cannon's 2 × 2 block parametrization and the input normal Riccati form parametrization. An over-parametrization formulation is also proposed. Numerical experiments suggest that the combination of a globally convergent homotopy method and a minimal parameter formulation applied to the upper bound minimization gives excellent results for mixed-norm H2/H∞ synthesis. The non-monotonicity of homotopy zero curves is demonstrated, proving that algorithms more sophisticated than standard continuation are necessary.

Probability-one homotopy algorithms for full- and reduced-orderH2/H∞ controller synthesis

Homotopy algorithms for both full- and reduced-order LQG controller design problems with an H∞ constraint on disturbance attenuation are developed. The H∞ constraint is enforced by replacing the covariance Lyapunov equation by a Riccati equation whose solution gives an upper bound on H 2 performance. The numerical algorithm, based on homotopy theory, solves the necessary conditions for a minimum of the upper bound on H 2 performance. The algorithms are based on two minimal parameter formulations : Ly, Bryson and Cannon's 2 x 2 block parametrization and the input normal Riccati form parametrization. An overparametrization formulation is also proposed. Numerical experiments suggest that the combination of a globally convergent homotopy method and a minimal parameter formulation applied to the upper bound minimization gives excellent results for mixed-norm H 2 /H∞ synthesis. The nonmonotonicity of homotopy zero curves is demonstrated, proving that algorithms more sophisticated than standard continuation are necessary.

Iterative LQG Controller Design Through Closed-Loop Identification

This paper presents an iterative LQG controller design approach for a linear stochastic system with an uncertain openloop model and unknown noise statistics. This approach consists of closed-loop identification and controller redesign cycles. In each cycle, the closed-loop identification method is used to identify an open-loop model and a steady-state Kalman filter gain from closed-loop input/output test data obtained by using a feedback LQG controller designed from the previous cycle. Then the identified open-loop model is used to redesign the state feedback. The state feedback and the identified Kalman filter gain are used to form an updated LQG controller for the next cycle. This iterative process continues until the updated controller converges. The proposed controller design is demonstrated by numerical simulations and experiments on a highly unstable large-gap magnetic suspension system.