Extension and Simplification of Salukvadze’s Solution to the Deterministic Nonhomogeneous LQR Problem

1998 ◽  
Vol 123 (1) ◽  
pp. 146-149
Author(s):  
R. D. Hampton ◽  
C. R. Knospe ◽  
M. A. Townsend
Keyword(s):  
Dynamic Systems ◽  
Variational Calculus ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Matrix Methods ◽  
Lqr Problem ◽  
Asme Journal ◽  
Analytic Design ◽  
And Control ◽  
Measurement And Control

In a previous paper (Hampton, R. D., et al., 1996, “A Practical Solution to the Deterministic Nonhomogeneous LQR Problem,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 118, pp. 354–360.) the authors presented a solution to the nonhomogeneous linear-quadratic-regulator (LQR) problem, for the case of known, deterministic, persistent (“non-dwindling”) disturbances. The authors used variational calculus and state-transition-matrix methods to produce an optimal matric solution, for bounded determinist forcing terms. A restricted version of this problem (treating dwindling disturbances) was evidently first investigated by Salukvadze, M. E., 1962, “Analytic Design of Regulators (Constant Disturbance),” Automation and Remote Control, Vol. 22, No. 10, Mar., pp. 1147–1155, using a differential-equations approach. The present paper uses Salukvadze’s approach to extend his work to the case of non-dwindling disturbances, with cross-weightings between state- and control vectors, and pursues the solution to the same form reported previously in Hampton et al.

Design of a vibration-free platform: Stabilization of a beam mounted on bicycle model of a car

2017 ◽  
Vol 232 (22) ◽  
pp. 4113-4127
Author(s):  
CU Dogruer ◽  
Bora Yildirim
Keyword(s):  
Mixed Finite Element ◽  
Linear Quadratic Regulator ◽  
Lumped Parameter Model ◽  
Linear Quadratic ◽  
High Precision Measurement ◽  
Lumped Parameter ◽  
Bicycle Model ◽  
Control Devices ◽  
And Control ◽  
Measurement And Control

Many high-precision measurement and control devices must be mounted on vibration-free platforms. Accuracy of those devices’ output are adversely affected by the base excitation motion, so motion of these platforms must be isolated from the excitation source. In this paper, a flexible platform, which is mounted on a car, is considered as a base on which many such measurement and control devices can be attached. To this end, mixed finite element and lumped parameter model of the platform and vehicle are used to derive the model of such a system; this results in a discrete-model with finite degree of freedom. This lumped parameter model of the system is then controlled by a linear quadratic regulator, which minimizes the amplitude of vibration at finite number of points on the platform. The mathematical model of this system was simulated on a computer and it has been shown that it is possible to minimize the vibration of this flexible platform.

scholarly journals Mathematical Modelling and Control of a Two-Wheeled PUMA-LikeVehicle

2016 ◽  
Vol 6 (2) ◽  
pp. 11 ◽  
Author(s):  
Khaled M Goher
Keyword(s):  
Mathematical Modelling ◽  
Sliding Mode ◽  
Impact Load ◽  
State Space Model ◽  
Linear Quadratic Regulator ◽  
The Body ◽  
Pole Placement ◽  
General Motors ◽  
Linear Quadratic ◽  
And Control

<p class="1Body">This paper presents mathematical modelling and control of a two-wheeled single-seat vehicle. The design of the vehicle is inspired by the Personal Urban Mobility and Accessibility (PUMA) vehicle developed by General Motors® in collaboration with Segway®. The body of the vehicle is designed to have two main parts. The vehicle is activated using three motors; a linear motor to activate the upper part in a sliding mode and two DC motors activating the vehicle while moving forward/backward and/or manoeuvring. Two stages proportional-integral-derivative (PID) control schemes are designed and implemented on the system models. The state space model of the vehicle is derived from the linearized equations. Controller based on the Linear Quadratic Regulator (LQR) and the pole placement techniques are developed and implemented. Further investigation of the robustness of the developed LQR and the pole placement techniques is emphasized through various experiments using an applied impact load on the vehicle.</p>

Modeling and Control of a Complex Interacting Process

2011 ◽  
Vol 403-408 ◽  
pp. 3758-3762
Author(s):  
Subhajit Patra ◽  
Prabirkumar Saha
Keyword(s):  
Storage System ◽  
Linear Quadratic Regulator ◽  
Model Parameters ◽  
Linear Quadratic ◽  
Modeling And Control ◽  
Dynamic Matrix ◽  
Liquid Storage ◽  
Efficient Control ◽  
And Control

In this paper, two efficient control algorithms are discussed viz., Linear Quadratic Regulator (LQR) and Dynamic Matrix Controller (DMC) and their applicability has been demonstrated through case study with a complex interacting process viz., a laboratory based four tank liquid storage system. The process has Two Input Two Output (TITO) structure and is available for experimental study. A mathematical model of the process has been developed using first principles. Model parameters have been estimated through the experimentation results. The performance of the controllers (LQR and DMC) has been compared to that of industrially more accepted PID controller.

Acoustic Control Modeling of Conical Bores With Actuating Boundary Conditions

2001 ◽  
Author(s):  
Kevin M. Farinholt ◽  
Donald J. Leo
Keyword(s):  
Boundary Conditions ◽  
Driving Forces ◽  
State Space Model ◽  
Linear Quadratic Regulator ◽  
Mode Shapes ◽  
Linear Quadratic ◽  
Acoustic Control ◽  
Average Control ◽  
The One ◽  
And Control

Abstract An investigation of the natural frequencies and mode shapes associated with sealed conical bores having actuating boundary conditions is presented. Beginning with the one dimensional wave equation for spherically expanding waves, modal characteristics are developed as functions of cone geometry and actuator parameters. This paper presents both analytical and experimental comparisons for the purpose of validating model and development techniques. An investigation of the orthogonality and adjointness of the solution is presented. A discussion of incorporating driving forces in the system model for the purpose of coupling control actuators with internal acoustics is also included. Including these driving forces, a state space model of the system is developed for the purpose of applying modern feedback control. This paper concludes with a study on applying Linear Quadratic Regulator techniques to this system, relating tradeoffs between spatially averaged pressure and control voltages. The results of our simulations indicate that pressure reductions of 30% are attainable with average control voltages of 14.4 volts, given an example geometry.

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