Linear Quadratic Gaussian Method Research Articles

Theoretical and experimental investigations on an active control system for vertical fin buffeting alleviation using strain actuation

AbstractIn the present investigation, the results obtained during the ground vibration tests of a closed-loop control system conducted on a full-scale fighter to attenuate vertical fin buffeting response using strain actuation are presented. The experimental results are supported by numerical analyses using a finite element aeroelastic model of the structure. Two groups of actuators consisting of piezoelectric elements distributed over the structure were designed to achieve authority over the first and second modes of the vertical fin. The control laws were synthesised using the linear quadratic Gaussian (LQG) method for a time-invariant two-input, two-output (2x2 MIMO) control system. Three different pairs of sensors including strain gauges and accelerometers at different locations were used to close the feedback loop. The results demonstrated that actual reductions of up to 18% in the root-mean-square (RMS) values of the fin dynamic response measured by the strain transducer at the critical point for fatigue at the root were achieved for the second mode under the most severe buffet condition.

Robust control of sound in an active acoustic grillage

This study evaluates the results of robust control of an active acoustic grillage (AAG). The AAG is an array of sound sources and microphones forming an acoustic barrier trapping sound but allowing air and light to pass through. Due to strong coupling between the cells of the AAG and resulting acoustic ‘‘feedback,’’ a multivariable H∞-synthesis is used for the controller design to yield a stable and robust closed loop system. The multi-input–multi-output (MIMO) design is compared with a linear-quadratic-Gaussian (LQG) design and a classical SISO approach that neglects the cross-coupling between the cells. System modeling, H∞-synthesis including the weight selection, simulation and implementation issues are discussed. The H∞-controller is tested on a four-cell grillage installed on the rectangular duct with cross section 50×50 cm. The robust controller provides 10–12-dB attenuation in the frequency range of 100–300 Hz that is superior to performance achieved with LQG or SISO methods. The controller implementation includes additional features like calibration and real-time monitoring. The work demonstrates benefits of robust MIMO design in noise control systems with multiple sensors and actuators where cross coupling is significant.

Real-time control of reactive ion etching using neural networks

This paper explores the use of neural networks for real-time, model-based feedback control of reactive ion etching (RIE). This objective is accomplished in part by constructing a predictive model for the system that can be approximately inverted to achieve the desired control. An indirect adaptive control (IAC) strategy is pursued. The IAC structure includes a controller and plant emulator, which are implemented as two separate back-propagation neural networks. These components facilitate nonlinear system identification and control, respectively. The neural network controller is applied to controlling the etch rate of a GaAs/AlGaAs metal-semiconductor-metal (MSM) structure in a BCl/sub 3//Cl/sub 2/ plasma using a Plasma Therm 700 SLR series RIE system. Results indicate that in the presence of disturbances and shifts in RIE performance, the IAC neural controller is able to adjust the recipe to match the etch rate to that of the target value in less than 5 s. These results are shown to be superior to those of a more conventional control scheme using the linear quadratic Gaussian method with loop-transfer recovery, which is based on a linearized transfer function model of the RIE system.

Internal model-based LQG/H/sub ∞/ design of robust active noise controllers for an acoustic duct system

In this paper, a method of linear quadratic Gaussian (LQG) control with an H/sub /spl infin// performance bound is modified for a robust active noise control design of an acoustic duct system. This H/sub /spl infin//-constraint LQG (LQG/H/sub /spl infin//) method is incorporated with an internal model principle to design robust internal model-based active noise controllers to attenuate a narrow-band disturbance noise in a duct. Computer simulation results show an enhanced robust control performance of this internal model-based LQG/H/sub /spl infin// design with respect to the variation of the disturbance noise frequency and demonstrate a global control performance along the duct. Experimental results further demonstrate its global performance robustness capability and support the feasibility of the proposed internal model-based LQG/H/sub /spl infin// design method.

LQG and GA solutions for active steering of railway vehicles

The paper presents control strategies for the active steering of solid axle railway vehicles using the linear quadratic Gaussian (LQG) method. The paper investigates the benefits of actively controlling and steering the wheelsets of a railway vehicle and studies what could be achieved when modern control techniques are used on the vehicles via mechatronic components. An optimal H2 controller is developed for the active steering and is fine-tuned using genetic algorithms. A Kalman filter is developed to provide the full state feedback required by the optimal control. The Kalman filter is formulated in such a way that it not only estimates all the vehicle states, but also calculates parameters such as curve radius and cant of the railway track on which the vehicle is travelling. Computer simulations are used in the study to assess the system performance with the control scheme proposed.

LQG/GA DESIGN OF ACTIVE NOISE CONTROLLERS FOR A COLLOCATED ACOUSTIC DUCT SYSTEM

Active noise control of an acoustic duct system is studied by a real state-space model in this paper. The linear quadratic Gaussian (LQG) method is chosen to design an active noise controller in order to reject noise in a collocated duct system subject to a disturbance source at one end. Robustness property of the designed controller with respect to the uncertainty of a complex-valued acoustic impedance at the other end is validated through computer simulations. A nominal real-valued acoustic impedance is therefore used to design reduced order controllers. The design parameters of the LQG method are automatically adjusted by using a simple genetic algorithm (SGA) to achieve a better global control effect. This adjustment is guided by a fitness function of SGA specified by a control objective. Results from computer simulation demonstrate the global effectiveness of the active noise controllers. Results of experiments also support the feasibility of the proposed design method.

A design method of a generalized predictive control system based on parametrization of two‐degree‐of‐freedom integral controllers

A new design method for a generalized predictive control (GPC) system based on parametrization of two-degree-of-freedom integral controllers has been proposed. The objective is to guarantee stability of the control system without depending on the design parameters and to achieve low sensitivity against the plant perturbation and the disturbance. The design procedure consists of two steps. First, we design a basic integral controller for a nominal plant using the linear quadratic Gaussian (LQG) method and parametrize a class of two-degree-of-freedom stabilizing controllers. Next, we tune the feedforward controller to incorporate the GPC method into our control structure. A numerical example is presented to show the effectiveness of the proposed method by comparing it with the conventional GPC method. © 1999 Scripta Technica, Electr Eng Jpn, 129(2): 62–70, 1999

A design method of a generalized predictive control system based on parametrization of two-degree-of-freedom integral controllers

A new design method for a generalized predictive control (GPC) system based on parametrization of two-degree-of-freedom integral controllers has been proposed. The objective is to guarantee stability of the control system without depending on the design parameters and to achieve low sensitivity against the plant perturbation and the disturbance. The design procedure consists of two steps. First, we design a basic integral controller for a nominal plant using the linear quadratic Gaussian (LQG) method and parametrize a class of two-degree-of-freedom stabilizing controllers. Next, we tune the feedforward controller to incorporate the GPC method into our control structure. A numerical example is presented to show the effectiveness of the proposed method by comparing it with the conventional GPC method. © 1999 Scripta Technica, Electr Eng Jpn, 129(2): 62–70, 1999

Substructural control design for serial flexible structures using the linear quadratic Gaussian method

A substructural control technique is developed for serial flexible structures using the linear quadratic Gaussian control method. A flexible structure is suitably decomposed into substructures, and subcontrollers and subobservers are designed for the substructures. The subcontroller forces generated within the substructures are taken into account when designing the subcontrollers and subobservers, which are assembled to obtain the global controller and observer for the entire structure. The technique is illustrated with the aid of a numerical example, which demonstrates the accuracy of the proposed substructural control technique compared with the complete structural control technique. The substructural control technique is expected to yield great computational savings in the control design of large serial flexible structures with accuracy.

Evaluation of a Cascade Compensator for Horizontal Vibrations of a Flexible Spray Boom

Spray booms are weakly damped flexible structures. Tractor vibrations induce horizontal boom deformations which are one of the main causes of an uneven spray deposition. Since structural adaptations to suppress boom vibration present problems, the feasibility of an active vibration compensator was investigated in laboratory tests. The experimental structure consisted of a flexible hollow beam with properties representative of common small spray booms, and a cradle on which the beam was clamped. In the experiments, longitudinal tractor vibrations were imposed upon the cradle and flexible deformations of the beam, induced by cradle accelerations, were compensated by an electro-hydraulic control system. The linear quadratic Gaussian method with loop transfer recovery, a robust control theory, was used to design the compensator. Measured amplitudes of the beam vibrations were reduced by a factor of more than thirty by the electro-hydraulic compensator.

A modelling procedure for linearized motions of tree structured multibodies—2: Design of an active spray boom suspension on a spraying-machine

In part 1 of the paper, the linearized equations of motion of a multibody system have been established. In this part, the method is used to compute the equations of motion of a spraying-machine consisting of 10 bodies. Tyres are represented by the tyre model of Crolla. The contact length tyre-ground which determines the low-pass filtering quality for the tyres, is also taken into account. Through a smaller nominal model that has been derived directly from the multibody model, an active spray boom suspension is designed with the aid of the linear quadratic Gaussian method with loop transfer recovery. A hydraulic actuator counteracts undesired rolling of the tractor by rotating the spray boom in the opposite direction, such that the distance between the spray nozzles and the field crops remains within an acceptable range. In the simulations, compensated and uncompensated spray boom motions are generated by driving the machine over some incompressible standardized tracks and corresponding spray deposit distributions are generated.

Bank-to-turn optimal guidance with linear exponential quadratic Gaussian performance criterion

This paper presents an optimal guidance law for controlling the pitch acceleration and roll rate of a bankto-turn missile with linearized plant dynamics and zero autopilot lag. The closed-form solution of the guidance law is derived by using the linear exponential quadratic Gaussian performance criterion and the corresponding Hamilton-Jacobi-Bellman equation. In addition, a constant acceleration bias is also introduced to prevent excessive roll rate command due to noise. It is shown that the optimal control gain can explicitly take both system and measurement noise covariances into consideration; therefore, the average, maximum, and standard deviation of miss distance can be reduced. Comparisons with those optimal guidance laws developed by the traditional linear quadratic Gaussian method are also made, which prove that the proposed guidance law is always better.

Optimal controller design for discrete saturating systems

A design procedure is proposed for synthesizing a linear-quadratic-Gaussian (LQG) optimal controller to obtain excess robustness optimization against noise spectral uncertainties, non-linear time-varying (NLTV) unmodelled dynamics in the discrete saturating systems. A robust stability criterion is derived for multivariable stochastic discrete-time systems with NLTV unmodelled dynamics and constrained actuators. An algorithm based on the robust stabilization criterion is presented for synthesizing a robust controller not only to minimize the least favourable cost functional J but also to maximize the excess robustness with respect to H∞-norm criterion by selecting two adequate weighting matrices Q(z) and R(z). We shall adopt the transfer function approach and two weighting matrices in the cost functional are shaped via the inverse LQG method to achieve excess robustness optimization.

Closed-Loop Learning Control Using Coprime Factorization Approach.

In this paper, we propose a new design method for a learning control system. The objectives of this paper are to enhance the tracking performance of learning controllers and to suppress disturbances acting on a plant. The structure of the learning controller is based on the parametrization of all stabilizing controllers, which is called Youla parametrization. The design procedure is divided into two steps. First, we design a basic controller using the LQG (linear quadratic Gaussian) method and consider the parametrization based on the LQG controller. Then, we adjust the free parameter to obtain good tracking performance by the learning algorithm. A numerical example is given to illustrate the effectiveness of the proposed method.

Active Vibration Control for Aircraft Wing

In active vibration control, gust load alleviation and flutter suppression method are studied for aircraft. For this purpose, an aero-servoelastic analysis code was developed using the finite element code MSC/NASTRAN. Moreover, a control law synthesis method was developed and applied to the LQG (linear quadratic Gaussian) method for reduced-order control law design. To validate both aeroservoelastic analysis and the control law synthesis code, the wind tunnel test of gust load alleviation was conducted in a 2 m low-speed wind tunnel of Nagoya Aerospace Systems Works using an aeroelastic wind model equipped with an actively controlled trailing edge surface. Analytical results were compared with the results from tests, and good agreement was obtained for wing acceleration. To estimate the effects of gust load alleviation and flutter suppression, they were applied to a 150-passenger twin-engine commercial airplane. For gust load alleviation, a 46.9% wing bending moment reduction was caused, as well as a flutter suppression of 30.7% flutter speed augmentation.

Steady-state optimal controller with actuator noise variance linearly related to actuator signal variance

The linear-quadratic-Gaussian (LQG) method assumes that the covariance matrix of the actuator noise is given before the design of the feedback matrix. However, in practice, the actuator-noise covariance matrix may depend on the actuator signal energy, which depends on the feedback. Consequently, the feedback from LQG theory degrades the system performance. The authors investigate the steady-state optimal controller when the noise variance of an actuator is linearly related to the variance of an actuator signal. This control system could be much more precise and/or spend much less control energy than the one obtained through the use of the ordinary LQG method. >

Combined linear quadratic Gaussian and H-infinity control of a benchmark problem

A combined linear quadratic Gaussian and Hx design method is applied to a benchmark problem. Robust controllers are derived that minimize an upper bound of a quadratic performance index subject to an Hx norm bound on a disturbance transfer function matrix. Real parameter variations are included in the design through the addition of fictitious weighted disturbances. Three design cases, each with different robustness, performance, and disturbance rejection requirements, are considered for the benchmark problem. Uncertain parameters and noncollocation of the sensor and actuator make the problem nontrivial. Compensators are found that meet the requirements with reasonable control effort, controller complexity, and noise rejection.

Active Vibration Control Technology for Aircraft Wing.

In active vibration control technology, gust load alleviation and flutter suppression technologies are studied for aircraft. For this purpose, an aero-servoelastic analysis code was developed using the MSC/NASTRAN by MHI. Moreover, a control low-synthesis method was developed, being applied to LQG (linear quadratic Gaussian) method for reduced order control law design. To validate both the aeroservoelastic analysis and the control law synthesis code, the wind tunnel test of gust load alleviation was conducted in a 2m low-speed wind tunnel of Nagoya Aerospace Systems Works using an aeroelastic wind model equipped with an actively controlled trailing edge surface. Analysis results were compared with the results from tests and good agreement with test results was obtained for the wing acceleration. To estimate the effects of gust load alleviation and flutter suppression technologies, they were applied to a 150-passenger twin-engine commercial airplane. For gust load alleviation, a 46.9% wing bending moment reduction effect was presented and flutter suppression, 30.7% flutter speed augmentation effect was presented.

Control of a 2-link flexible arm. 1st reoprt, Evaluation of the robust stability against the spillover and experiments on an active demping control.

An active damping control method has been applied to achieve quick positioning for a 2-link flaxible manipulator. The 2-link flexible manipulator is regarded as a distributed parameter model in consideration of mutual interaction between links. On this model the LQG(linear quadratic Gaussian) method, composed of a Kalman filter and an optimal regulator, has been applied to an active damping controller. In tuning the LQG controller, the robustness against the spillover has been evaluated in the frequency domain to confirm the stability of the closed loop system. Using the testing model, the following results were obtained : (1) The 1st mode of the vibration was completely damped. (2) The positioning time was reduced by 1/5 compared to that of the conventional control method, which feedbacks position and velocity signal of each joint.

Robust linear quadratic Gaussian control for flexible structures

A procedure is developed to deal with performance and robustness issues in the design of multiple-input multiple-output compensators for lightly damped flexible structures. The procedure is based upon representing errors in the plant design model as structured uncertainties, and applying a modified linear quadratic Gaussian design method. The cost function in the regulator problem and the process noise model in the estimator problem are varied in a manner that reflects specific parameter uncertainty including frequency, damping, or modal displacement errors. Numerical examples dealing with the control of a large flexible space antenna with uncertain frequencies demonstrate the application of the method.