Modeling and Control of Surface Quality in Chemical Mechanical Planarization (CMP)

2017 ◽  
Author(s):  
Pavan Poosarla ◽  
Hamid Emadi ◽  
Abhijit Chandra ◽  
Sourabh Bhattacharya
Keyword(s):  
State Space ◽  
Control Strategies ◽  
Chemical Mechanical Planarization ◽  
State Space Model ◽  
Closed Form Solution ◽  
Surface Profile ◽  
Open Loop ◽  
Form Solution ◽  
Machining Process ◽  
Loop Control

Obtaining uniform surface finish across large length scales is extremely important in Chemical Mechanical Planarization (CMP). Existing control strategies use results from model simulations to propose open-loop control strategies to reduce the step height on surfaces being polished. In the present work, we propose a strategy to control the surface profile of substrate during CMP process. The evolution of the surface profile is predicted using the state space model of the polishing process. The resulting state space equation is solved and a closed form solution of the surface profile is obtained as a function of time. Based on the solution, we provide a fundamental limitation for the machining process in terms of the extent of planarization that can be achieved for a given material budget.

scholarly journals Euler-Maclaurin Closed Form Finite State Space Model for a String Applied to Broadband Plate Vibrations

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Michael J. Panza
Keyword(s):  
Closed Form ◽  
State Space ◽  
State Space Model ◽  
Closed Form Solution ◽  
String Model ◽  
Form Solution ◽  
Space Model ◽  
Function Solution ◽  
Plate Vibrations ◽  
Finite State

The Euler-Maclaurin sun formula is applied to the infinite series Green's function solution in the space-time Laplace transform domain for the one dimensional wave equation for a string fixed at each end. The resulting approximate closed form solution is used to derive a single third order input-output ordinary differential equation to model the string dynamics. The average modal density of a plate is shown to be comparable to a string. A finite three state-space model is developed for the string and applied to the vibrations of a plate subjected to broadband random and impulse inputs. The applications include the direct problem of determining the response to a disturbance input and the inverse problem of identifying the disturbance input with a finite state observer based on the finite string model. Numerical simulations using many plate modes are obtained in the time and frequency domains and are used to compare the multimodal plate model to the finite string based model and to demonstrate how the finite string based model can be used to represent the multimodal vibrations of the plate.

scholarly journals On the optimal control of affine nonlinear systems

2005 ◽  
Vol 2005 (4) ◽  
pp. 465-475 ◽  
Author(s):  
M. Popescu ◽  
A. Dumitrache
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Lie Algebra ◽  
Closed Form Solution ◽  
Bilinear System ◽  
Open Loop ◽  
Form Solution ◽  
Loop Control ◽  
Nilpotent Operators ◽  
Affine Nonlinear Systems

The minimization control problem of quadratic functionals for the class of affine nonlinear systems with the hypothesis of nilpotent associated Lie algebra is analyzed. The optimal control corresponding to the first-, second-, and third-order nilpotent operators is determined. In this paper, we have considered the minimum fuel problem for the multi-input nilpotent control and for a scalar input bilinear system for such systems. For the multi-input system, usually an analytic closed-form solution for the optimal controlui∗(t)is not possible and it is necessary to use numerical integration for the set ofmnonlinear coupled second-order differential equations. The optimal control of bilinear systems is obtained by considering the Lie algebra generated by the system matrices. It should be noted that we have obtained an open-loop control depending on the initial value of the statex0.

Yield Improvement via minimization of step height non-uniformity in Chemical Mechanical Planarization (CMP)

2005 ◽  
Vol 867 ◽  
Author(s):  
Muthukkumar Kadavasal ◽  
Sutee Eamkajornsiri ◽  
Abhijit Chandra ◽  
Ashraf F. Bastawros
Keyword(s):  
Chemical Mechanical Planarization ◽  
Open Loop ◽  
Step Height ◽  
Control Algorithms ◽  
Open Loop Control ◽  
Time Step ◽  
Surface Evolution ◽  
Loop Control ◽  
Final Surface ◽  
Pattern Density

AbstractObtaining local and global planarity is one of the prime criteria in dielectric and metal planarizations. Although Chemical Mechanical Planarization (CMP) helps us achieve this criterion in constant pattern density surfaces, the same is not true for variable pattern density surfaces this results in formation of global step heights across the die. This paper provides a pressure open loop control algorithms for obtaining planarity across a die containing variations in pattern densities. Based on the variation of pattern density and surface heights across the die, the surfaces are separated into zones and the pressure is varied spatially and/or temporally to obtain uniform surface heights, with enhanced step height uniformity. One of the algorithms looks ahead and recalculates/modifies the pressure values by identifying the step heights that could be formed after a specified time step. The final surface predictions have improved uniformity on the upper surface as well as on the step heights across the entire die. The simulation would help us track the polishing process for each time step and guide us with the optimized pressure values that can be applied in order to an uniform final surface evolution.

Small Scale Wind Generation System: Part II – A Novel Quasi-Z-Source Inverter and FRG-QZSI-Micro Grid Interface

2017 ◽  
Vol 6 (1) ◽  
pp. 13
Author(s):  
M. Ramkumar ◽  
K. N. Srinivas
Keyword(s):  
Control Strategies ◽  
Research Work ◽  
Open Loop ◽  
Small Scale ◽  
Loop Control ◽  
Power Injection ◽  
System Part ◽  
Micro Grid ◽  
Wind Generation System ◽  
And Control

<p>This paper proposes modelling, analysis and control of a small scale wind energy conversion system employing a direct driven Flux Reversal Generator (FRG) connected to the micro grid through a quasi-Z-source inverter (QZSI). This entire research is made up of two major parts viz., FRG and QZSI. In the part I report of this research work, the role of FRG has been thoroughly modelled and verified. In this part II, the modelling and analysis of QZSI for this purpose is presented. In addition, the modified space vector PWM (SVPWM) technique is proposed in this paper to satisfy the shoot-through characteristic of QZSI, which is a novel. The interface of FRG and QZSI to inject power in to micro grid has been finally presented. The simulation results are validated with the analytical results. Section I discusses the open loop control of QZSI. The mathematical modelling of QZSI for this purpose is given and analytically validated. This flowed by section II in which the proposed SVPWM is presented. The procedure to obtain triggering pulses using this proposed modulation technique is discussed. Section III presents closed loop control strategies for QZSI. Section IV presents the micro grid<br />inte face and power injection.</p>

scholarly journals Model Predictive Control with a Relaxed Cost Function for Constrained Linear Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
David Sotelo ◽  
Antonio Favela-Contreras ◽  
Viacheslav V. Kalashnikov ◽  
Carlos Sotelo
Keyword(s):  
Model Predictive Control ◽  
Cost Function ◽  
State Space ◽  
Predictive Control ◽  
Discrete Time ◽  
Control Strategy ◽  
Control Strategies ◽  
State Space Model ◽  
Control Technique ◽  
Space Model

The Model Predictive Control technique is widely used for optimizing the performance of constrained multi-input multi-output processes. However, due to its mathematical complexity and heavy computation effort, it is mainly suitable in processes with slow dynamics. Based on the Exact Penalization Theorem, this paper presents a discrete-time state-space Model Predictive Control strategy with a relaxed performance index, where the constraints are implicitly defined in the weighting matrices, computed at each sampling time. The performance validation for the Model Predictive Control strategy with the proposed relaxed cost function uses the simulation of a tape transport system and a jet transport aircraft during cruise flight. Without affecting the tracking performance, numerical results show that the execution time is notably decreased compared with two well-known discrete-time state-space Model Predictive Control strategies. This makes the proposed Model Predictive Control mainly suitable for constrained multivariable processes with fast dynamics.

Point Control of a One-Link Flexible Manipulator

1986 ◽  
Vol 53 (1) ◽  
pp. 23-27 ◽  
Author(s):  
S. B. Skaar ◽  
D. Tucker
Keyword(s):  
Transfer Functions ◽  
Control Strategies ◽  
Open Loop ◽  
Flexible Manipulator ◽  
Distributed Parameter ◽  
Loop Control ◽  
Control Approach ◽  
Alternative Approach ◽  
Single Link ◽  
Point Control

An alternative approach to the control of nonrigid, distributed parameter systems is presented. Transfer functions that relate the response of points on the system to a controlling force or torque are used in place of ordinary differential equations, which represent an approximation to the system dynamics. The implications of this “point control” approach are discussed with regard to plant modeling accuracy, uncontrolled regions, open-loop and closed-loop control strategies, system identification, and feedback estimation. Sample optimal control histories are illustrated for a single-link manipulator member with end load.

scholarly journals Control of Flexible Manipulator Systems

1996 ◽  
Vol 210 (2) ◽  
pp. 113-130 ◽  
Author(s):  
M O Tokhi ◽  
A K M Azad
Keyword(s):  
Closed Loop ◽  
Control Strategies ◽  
Open Loop ◽  
Flexible Manipulator ◽  
Closed Loop Control ◽  
Loop Control ◽  
Acceleration Feedback ◽  
Low Pass ◽  
Input Torque ◽  
Collocated Control

This paper presents an investigation into the development of open-loop and closed-loop control strategies for flexible manipulator systems. Shaped torque inputs, including Gaussian-shaped and low-pass (Butter-worth and elliptic) filtered input torque functions, are developed and used in an open-loop configuration and their performance studied in comparison to a bang-bang input torque through experimentation on a single-link flexible manipulator system. Closed-loop control strategies that use both collocated (hub angle and hub velocity) and non-collocated (end-point acceleration) feedback are then proposed. A collocated proportional and derivative (PD) control is first developed and its performance studied through experimentation. The collocated control is then extended to incorporate, additionally, non-collocated feedback through a proportional integral derivative (PID) configuration. The performance of the hybrid collocated and non-collocated control strategy thus developed is studied through experimentation. Experimental results verifying the performance of the developed control strategies are presented and discussed.

Identification of Stochastic System and Controller via Projection Filters

1996 ◽  
Vol 118 (2) ◽  
pp. 169-176 ◽  
Author(s):  
Hyun Chang Lee ◽  
Min-Hung Hsiao ◽  
Jen-Kuang Huang ◽  
Chung-Wen Chen
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Stochastic System ◽  
State Space Model ◽  
Open Loop ◽  
The State ◽  
Loop System ◽  
Test Facility ◽  
System Response ◽  
Space Model

A method based on projection filters is presented for identifying an open-loop stochastic system with an existing feedback controller. The projection filters are derived from the relationship between the state-space model and the AutoRegressive with eXogeneous input (ARX) model including the system, Kalman filter and controller. Two ARX models are identified from the control input, closed-loop system response and feedback signal using least-squares method. Markov parameters of the open-loop system, Kalman filter and controller are then calculated from the coefficients of the identified ARX models. Finally, the state-space model of the open-loop stochastic system and the gain matrices for the Kalman filter and controller are realized. The method is validated by simulations and test data from an unstable large-angle magnetic suspension test facility.

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