Modeling and Multivariable Control of a High Precision Multidimensional Positioner

2004 ◽  
Author(s):  
Tiejun Hu ◽  
Won-Jong Kim
Keyword(s):  
High Precision ◽  
State Space Model ◽  
Maximum Velocity ◽  
Experimental Results ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Electromagnetic System ◽  
Position Resolution ◽  
Reduced Order ◽  
Linear Quadratic Regulation

A precision positioner using a novel concentrated-field permanent-magnet matrix is presented in this paper. This integrated multidimensional positioner is actuated by three novel planar motors, which are attached on the bottom of the positioner. It can generate all 6-DOF motions with only a single moving part. The integrated multi-dimensional positioner offers a unique combination of range and precision: a planar traveling range of 160 mm × 160 mm with a position resolution of 30 nm and position noise of 10 nm rms. The repeatability of the positioner is as good as 30 nm. The maximum velocity achieved so far is 0.5 m/s with 5-m/s2 acceleration. With direct-quadrature (DQ) decomposition theory, the positioner is modelled as a multi-input multi-output (MIMO) electromagnetic system: it has six inputs (currents) and six outputs (displacements). After the state-space model of the system is derived, multivariable controllers are designed for this high-precision positioner. To eliminate the steady-state error, discrete time integrator combined Linear Quadratic Regulation (LQR) and reduced order Linear Quadratic Gaussian (LQG) control methodologies are applied and implemented. Finally, the experimental results are presented in this paper. Several experimental results verified the utility of this positioner in precision applications, such as semiconductor manufacturing.

scholarly journals Multimodeling Control via System Balancing

2010 ◽  
Vol 2010 ◽  
pp. 1-20
Author(s):  
Nada Ratković Kovačević ◽  
Dobrila Škatarić
Keyword(s):  
Power Plants ◽  
Order Reduction ◽  
Reduced Order Models ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Reduced Order ◽  
Reduction Techniques ◽  
Balanced Model ◽  
Balancing Transformation ◽  
Different Order

A new approach in multimodeling strategy is proposed. Multimodel strategies in which control agents use different simplified models of the same system are being developed using balancing transformation and the corresponding order reduction concepts. Traditionally, the multimodeling concept was studied using the ideas of multitime scales (singular perturbations) and weak subsystem coupling. For all reduced-order models obtained, a Linear Quadratic Gaussian (LQG) control problem was solved. Different order reduction techniques were compared based on the values of the optimized criteria for the closed-loop case where the full-order balanced model utilizes regulators calculated to be the optimal for various reduced-order models. The results obtained were demonstrated on a real-world example: a multiarea power system consisting of two identical areas, that is, two identical power plants.

LQG Control for Nonstandard Singularly Perturbed Discrete-Time Systems

2004 ◽  
Vol 126 (4) ◽  
pp. 860-864 ◽  
Author(s):  
Beom-Soo Kim ◽  
Young-Joong Kim ◽  
Myo-Taeg Lim
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discrete Time ◽  
Singularly Perturbed ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Reduced Order ◽  
Discrete Time Systems ◽  
Time Systems

In this paper we present a control method and a high accuracy solution technique in solving the linear quadratic Gaussian problems for nonstandard singularly perturbed discrete time systems. The methodology that exists in the literature for the solution of the standard singularly perturbed discrete time linear quadratic Gaussian optimal control problem cannot be extended to the corresponding nonstandard counterpart. The solution of the linear quadratic Gaussian optimal control problem is obtained by solving the pure-slow and pure-fast reduced-order continuous-time algebraic Riccati equations and by implementing the pure-slow and pure-fast reduced-order Kalman filters. In order to show the effectiveness of the proposed method, we present the numerical result for a one-link flexible robot arm.

Design and Control of a 6-DOF Positioner With High Precision

2003 ◽  
Author(s):  
Wong-Jong Kim ◽  
Tiejun Hu ◽  
Nikhil Bhat
Keyword(s):  
High Precision ◽  
Digital Signal Processor ◽  
Maximum Velocity ◽  
Digital Signal ◽  
Position Resolution ◽  
Manufacturing Applications ◽  
Force Components ◽  
20 Nm ◽  
And Control ◽  
Matrix Base

This paper presents the design and construction of a 6-degree-of-freedom (6-DOF) multi-dimensional positioner. This positioner is based on a novel concentrated-field magnet matrix, and its electromagnetic operational principle is presented. This high-precision positioning system consists of a magnet-matrix base and a triangular single-moving platen that carries three 3-phase permanent-magnet linear levitation motor stators. With a combination of six independent force components, the moving platen can generate any 6-DOF motion. Three aerostatic bearings are used to provide the suspension force against gravity for the system. We designed and implemented digital lead-lag controllers running on a digital signal processor (DSP). Currently, the positioner has a position resolution of 20 nm and position noise of 10 nm rms. The planar traveling range is 160 mm × 160 mm and the maximum velocity achieved so far is 0.5 m/s with 5-m/s2 acceleration in the y-direction, which is highly suitable for semiconductor manufacturing applications. Several 2-dimensional motion profiles are presented to demonstrate the stage’s capability of accurately tracking any extended planar paths.

scholarly journals Synthesis of an Optimal Dynamic Regulator Based on Linear Quadratic Gaussian (LQG) for the Control of the Relative Humidity under Experimental Greenhouse

2016 ◽  
Vol 6 (5) ◽  
pp. 2262
Author(s):  
M. Outanoute ◽  
A. Lachhab ◽  
A. Ed-dahhak ◽  
M. Guerbaoui ◽  
A. Selmani ◽  
...  
Keyword(s):  
Relative Humidity ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Monitoring And Control ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
State Space System ◽  
Optimal Dynamic ◽  
And Control

<p><span lang="EN-US">This paper describes one practical approach that suggests a model based technique to control in real time the relative humidity under greenhouse. The humidity level is one of the most difficult environmental factors to be regulated in greenhouse. Moreover, maintaining and correcting for more or less humidity can be a challenge for even the most sophisticated monitoring and control equipment. For these raisons, a Linear Quadratic Gaussian (LQG) controller for relative humidity regulation under greenhouse turns out to be useful. Indeed a LQG controller is proposed for a relative humidity under a greenhouse control task. So, the state space model, which is best fitting the acquired data, was identified using the Numerical Subspace State Space System IDentification (N4SID) algorithm. The mathematical model that is obtained will be used for evaluating the parameters of LQG strategy. The proposed controller is implemented in two steps, in one hand, Kalman filter (KF) is used to develop an observer that estimates the state of relative humidity under greenhouse. In the other hand, the state feedback controller gain is estimated using a linear quadratic criterion function. The suggested optimal implemented controller using Matlab/Simulink environment is applied to an experimental greenhouse. We found, according to the results, that the controller is able to lead the inside relative humidity to the desired value with high accuracy, regardless of the external disturbances.</span></p>

Synthesis of an Optimal Dynamic Regulator Based on Linear Quadratic Gaussian (LQG) for the Control of the Relative Humidity under Experimental Greenhouse

2016 ◽  
Vol 6 (5) ◽  
pp. 2262 ◽  
Author(s):  
M. Outanoute ◽  
A. Lachhab ◽  
A. Ed-dahhak ◽  
M. Guerbaoui ◽  
A. Selmani ◽  
...  
Keyword(s):  
Relative Humidity ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Monitoring And Control ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
State Space System ◽  
Optimal Dynamic ◽  
And Control

<p><span lang="EN-US">This paper describes one practical approach that suggests a model based technique to control in real time the relative humidity under greenhouse. The humidity level is one of the most difficult environmental factors to be regulated in greenhouse. Moreover, maintaining and correcting for more or less humidity can be a challenge for even the most sophisticated monitoring and control equipment. For these raisons, a Linear Quadratic Gaussian (LQG) controller for relative humidity regulation under greenhouse turns out to be useful. Indeed a LQG controller is proposed for a relative humidity under a greenhouse control task. So, the state space model, which is best fitting the acquired data, was identified using the Numerical Subspace State Space System IDentification (N4SID) algorithm. The mathematical model that is obtained will be used for evaluating the parameters of LQG strategy. The proposed controller is implemented in two steps, in one hand, Kalman filter (KF) is used to develop an observer that estimates the state of relative humidity under greenhouse. In the other hand, the state feedback controller gain is estimated using a linear quadratic criterion function. The suggested optimal implemented controller using Matlab/Simulink environment is applied to an experimental greenhouse. We found, according to the results, that the controller is able to lead the inside relative humidity to the desired value with high accuracy, regardless of the external disturbances.</span></p>

COMPARISON OF HYSTERESIS CONTROL AND REDUCED ORDER LINEAR QUADRATIC REGULATOR CONTROL FOR POWER FACTOR CORRECTION USING DC–DC CUK CONVERTERS

2012 ◽  
Vol 21 (01) ◽  
pp. 1250002 ◽  
Author(s):  
M. G. UMAMAHESWARI ◽  
G. UMA ◽  
S. REDLINE VIJITHA
Keyword(s):  
Power Factor ◽  
Power Factor Correction ◽  
Linear Quadratic Regulator ◽  
Voltage Regulation ◽  
Experimental Results ◽  
Linear Quadratic ◽  
Reduced Order ◽  
Order Linear ◽  
Hysteresis Controller ◽  
Set Up

This paper focuses on a comparative study of a reduced order linear quadratic regulator control (ROLQR) and conventional variable frequency hysteresis controller (HC) for power factor correction, and their performances are compared. A prototype of front-end AC–DC converter followed by DC–DC Cuk converter controlled by a dSPACE signal processor was set up for 60 watts. Experimental results are presented to validate the simulation results. Simulation and experimental results reveal that ROLQR control can achieve good output voltage regulation and also provide improved robustness in shaping the input current in the presence of load variations when compared to conventional HC.

Linear Quadratic Gaussian Control Applied to WFAO Systems: Simulation and Experimental Results

2011 ◽  
Vol 17 (3) ◽  
pp. 302-315 ◽  
Author(s):  
Anne Costille ◽  
Cyril Petit ◽  
Jean-Marc Conan ◽  
Caroline Kulcsár ◽  
Henri-François Raynaud
Keyword(s):  
Experimental Results ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Systems Simulation
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