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    ํ”Œ๋ผ์ฆˆ๋งˆ ์‹๊ฐ ์žฅ์น˜๋ฅผ ์œ„ํ•œ ์ ์‘๋ชจ๋ธ์˜ˆ์ธก์ œ์–ด๊ธฐ์˜ ์„ค๊ณ„

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    ํ•™์œ„๋…ผ๋ฌธ (๋ฐ•์‚ฌ)-- ์„œ์šธ๋Œ€ํ•™๊ต ๋Œ€ํ•™์› : ๊ณต๊ณผ๋Œ€ํ•™ ํ™”ํ•™์ƒ๋ฌผ๊ณตํ•™๋ถ€(์—๋„ˆ์ง€ํ™˜๊ฒฝ ํ™”ํ•™์œตํ•ฉ๊ธฐ์ˆ ์ „๊ณต), 2019. 2. ์ด์œค์šฐ.The semiconductor etching process, which is one of the most critical processes in the manufacturing of semiconductors and one that comprises numerous steps, requires higher sophistication as 10 nm semiconductors are mass produced. Currently, the semiconductor etching process is mostly done by physical and/or chemical etching with plasma. In addition, the plasma etching is getting increasingly popular with the miniaturization of the process to a scale of less than 10 nm. The result of a plasma etching process is represented in the form of an etch profile which is determined by the plasma variables. Therefore, the performance of the process depends on these variables, and it is essential to measure and control them in real time. Although research on the control of plasma etching processes has been actively carried out, the plasma etching process strongly relies on the experience and skill level of seasoned engineers at the industry level. This is because a plasma-based system is very complicated and sensitive, and has a time-varying characteristics. However, even though previous studies show excellent results, they employed invasive diagnostic tools, and have single variable control schemes where a counter change of another plasma variable during control actions for other variables might occur due to the highly interactive plasma characteristics. Moreover, they did not consider the time-varying characteristics of plasma-based systems. Therefore, this thesis proposes a multivariable control strategy which can cope with interaction effects and a design of an adaptive model predictive controller which maintains its performance wherein systems vary with time. At first, the plasma variables which are considered as controlled variables were selected as the electron density and the electron temperature. This is because one of the etch profile, especially etch rate, can be expressed as functions of those plasma variables and the variables can be measured by the optical emission spectroscopy which is a non-invasive diagnostic tool. The plasma variables were paired with instrumental variables through singular value decomposition and relative gain array for constructing the optimal multivariable system model. Two parallel proportional integral derivative (PID) controllers were designed based on the output errors then conducted plasma variable control simulations. Through the simulations, the exist of interaction between the variables was obviously verified. For resolving the interaction effectively, decoupler controllers were applied to the PID controllers. As it performed the control experiment of the Ar plasma electron density and electron temperature excellently, the possibility of multivariable control of plasma-based system is demonstrated. In spite of the meaningful control results using the PID controllers, there are obvious limitations in relation to the exquisiteness and to the characteristics of decoupler controllers as it highly dependent to the accuracy of the system model. In order to maintain performance even in the case of a system change, an advanced control strategy is required and model predictive control can be an alternative. Therefore, a model predictive controller was designed where the Bayesian optimization is used as tuning method for the maximization of the exquisiteness. The controller verified its capability as it conducted Ar plasma electron density control in a drift-free system. However, the performance of it deteriorated in control simulations of time-varying systems and in a control experiment performed in a system where O2 plasma was injected into an Ar plasma system inducing the high nonlinearity. Therefore, a more advanced control strategy which can overcome the difficulty was required. In an adaptive control method, once the information from the system is entered into the adjustment mechanism part, the part makes a decision to deliver it to the controller. Then the controller is modified in accordance with the decision and releases the optimal control action. The typical adaptive control algorithm, which is the recursive least squares algorithm, was used in this thesis. Using the algorithm with Kalman filter interpretation, the time-delay effect which comes from the plasma etching reactor can be considered. The recursive model parameter estimator utilizing this algorithm was tuned by Bayesian optimization. When the recursive model parameter estimator detects changes of the system model parameters in real time and transmits it to the model predictive controller, the controller calculates the optimal manipulated variable based on the modified model. The adaptive model predictive controller performed the same simulations and experiment as those performed by the model predictive controller. Unlike the model predictive controller, the proposed controller performed control excellently even when the system changes over time. Numerically, it showed the improved control ability by 24.7% and 30.4% in terms of the mean absolute percentage error and the number of deviated sample, respectively compared to the conventional model predictive controller. These results demonstrate that the adaptive model predictive controller designed in this theses is invaluable for plasma-based system control and is the effective controller for the plasma etching reactor. It is expected to make a significant contribution to plasma-based processes that require high sophistication and flexibility.์ˆ˜ ๋งŽ์€ ๊ณต์ •์œผ๋กœ ์ด๋ฃจ์–ด์ง„ ๋ฐ˜๋„์ฒด ์ œ์กฐ ๊ณต์ • ๋‚ด์—์„œ ๊ฐ€์žฅ ํฐ ๋น„์ค‘์„ ์ฐจ์ง€ํ•˜๊ณ  ์žˆ๋Š” ๋ฐ˜๋„์ฒด ์‹๊ฐ ๊ณต์ •์€ ์ตœ๊ทผ 10 nm๊ธ‰ ๋ฐ˜๋„์ฒด์˜ ์–‘์‚ฐ์ด ์ด๋ค„์ง์— ๋”ฐ๋ผ ์‹๊ฐ์˜ ๋†’์€ ์ •๊ต์„ฑ์ด ์š”๊ตฌ๋˜๊ณ  ์žˆ๋‹ค. ๋ฐ˜๋„์ฒด ์‹๊ฐ ๊ณต์ •์€ ํ˜„์žฌ ์‚ฐ์—…๊ณ„์—์„  ํ”Œ๋ผ์ฆˆ๋งˆ๋ฅผ ์ด์šฉํ•˜์—ฌ ๋ฌผ๋ฆฌ์ , ํ™”ํ•™์  ์‹๊ฐ์„ ์ผ์œผํ‚ค๋Š” ๋ฐฉ๋ฒ•์„ ํ†ตํ•ด ์ด๋ฃจ์–ด์ง€๊ณ  ์žˆ์œผ๋ฉฐ, ๊ณต์ •์ด 10 nm ๊ธ‰ ์ดํ•˜ ์Šค์ผ€์ผ๋กœ ๋ฏธ์„ธํ™”๋œ ํ›„๋กœ ์ด ๋ฐฉ๋ฒ•์ด ๋”์šฑ ๊ฐ๊ด‘ ๋ฐ›๊ณ  ์žˆ๋‹ค. ๊ณต์ •์˜ ๊ฒฐ๊ณผ๋Š” ์‹๊ฐ ํ”„๋กœํ•„์„ ๊ธฐ์ค€์œผ๋กœ ๊ฒฐ์ •๋˜๋Š” ๋ฐ ์ด ์‹๊ฐ ํ”„๋กœํ•„์ด ํ”Œ๋ผ์ฆˆ๋งˆ ๋ณ€์ˆ˜๋“ค์— ํฌ๊ฒŒ ์˜์กดํ•จ์ด ์ž…์ฆ๋จ์— ๋”ฐ๋ผ ์ด ๋ณ€์ˆ˜๋“ค์„ ์‹ค์‹œ๊ฐ„์œผ๋กœ ์ธก์ •ํ•˜๊ณ  ์ œ์–ดํ•˜๋Š” ๊ฒƒ์ด ๊ณต์ •์˜ ํ•ต์‹ฌ์ด ๋˜์—ˆ๋‹ค. ๊ทธ๋™์•ˆ ํ”Œ๋ผ์ฆˆ๋งˆ ๋ณ€์ˆ˜ ์ œ์–ด์— ๊ด€ํ•œ ์—ฐ๊ตฌ๋“ค์ด ํ™œ๋ฐœํžˆ ์ง„ํ–‰๋˜์–ด ์™”์œผ๋‚˜ ์•„์ง๊นŒ์ง€ ์‚ฐ์—…๊ณ„์—์„  ๊ทธ ์ด๋ก ๋“ค์„ ๋ฐ”๋กœ ํ™œ์šฉํ•˜์ง€ ๋ชปํ•˜๊ณ  ๊ฒฝํ—˜ ๋งŽ์€ ์—”์ง€๋‹ˆ์–ด์˜ ๊ฐ์— ์˜์กดํ•˜๊ณ  ์žˆ๋‹ค. ๊ทธ ์ด์œ ๋Š” ๊ทผ๋ณธ์ ์œผ๋กœ ์‹œ์Šคํ…œ์ด ๋งค์šฐ ๋ณต์žกํ•˜๊ณ  ์˜ˆ๋ฏผํ•  ๋ฟ ์•„๋‹ˆ๋ผ ์‹œ๊ฐ„์— ๋”ฐ๋ผ ๋ณ€ํ•˜๋Š” ํŠน์„ฑ์„ ๊ฐ–๊ณ  ์žˆ๊ธฐ ๋•Œ๋ฌธ์ด๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ์ด์ „์˜ ์—ฐ๊ตฌ๋“ค์€ ํ›Œ๋ฅญํ•œ ๊ฒฐ๊ณผ๋ฅผ ๋ณด์˜€์Œ์—๋„ ๋ถˆ๊ตฌํ•˜๊ณ , ํ”Œ๋ผ์ฆˆ๋งˆ ์‹œ์Šคํ…œ์— ์ง์ ‘์ ์œผ๋กœ ์˜ํ–ฅ์„ ๋ฏธ์น˜๋Š” ์นจํˆฌ์„ฑ ์„ผ์„œ๋ฅผ ์ด์šฉํ–ˆ๊ฑฐ๋‚˜, ํ”Œ๋ผ์ฆˆ๋งˆ ๋ณ€์ˆ˜๋“ค๊ณผ ์žฅ์น˜ ๋ณ€์ˆ˜๋“ค์ด ์„œ๋กœ ๋ณต์žกํ•˜๊ฒŒ ์–ฝํ˜€ ์žˆ์–ด ์•ผ๊ธฐ๋˜๋Š” ์ƒํ˜ธ์ž‘์šฉ์„ ๊ฐ„๊ณผํ•  ์ˆ˜๋ฐ–์— ์—†๋Š” ๋‹จ๋ณ€์ˆ˜ ์ œ์–ด๋ฅผ ์ˆ˜ํ–‰ํ•œ ๋ฐ์— ๊ทธ์น˜๊ณ  ์žˆ๋‹ค. ๊ฒŒ๋‹ค๊ฐ€ ์™ธ๋ž€ ๋•Œ๋ฌธ์— ๋ฐœ์ƒ๋˜๋Š” ์‹œ๊ฐ„์— ๋”ฐ๋ผ ๋ณ€ํ•˜๋Š” ํŠน์„ฑ์„ ๊ณ ๋ คํ•˜์ง€ ๋ชปํ•˜๊ณ  ์žˆ๋‹ค. ๋”ฐ๋ผ์„œ, ๋ณธ ํ•™์œ„๋…ผ๋ฌธ์—์„œ๋Š” ๋ณ€์ˆ˜๊ฐ„ ์ƒํ˜ธ์ž‘์šฉ์„ ์ตœ์†Œํ™”ํ•˜๋Š” ๋‹ค๋ณ€์ˆ˜ ์ œ์–ด ์ „๋žต๊ณผ ์‹œ์Šคํ…œ์ด ์‹œ๊ฐ„์— ๋”ฐ๋ผ ๋ณ€ํ•˜๋Š” ์ƒํ™ฉ์—์„œ๋„ ์„ฑ๋Šฅ์ด ์•…ํ™”๋˜์ง€ ์•Š๋Š” ์ ์‘๋ชจ๋ธ์˜ˆ์ธก์ œ์–ด๊ธฐ์˜ ์„ค๊ณ„๋ฅผ ์ œ์•ˆํ•œ๋‹ค. ๋จผ์ €, ์ „์ž ๋ฐ€๋„์™€ ์ „์ž ์˜จ๋„๊ฐ€ ์ œ์–ด ๋Œ€์ƒ์ด ๋˜๋Š” ํ”Œ๋ผ์ฆˆ๋งˆ ๋ณ€์ˆ˜๋กœ ์„ ์ •๋˜์—ˆ๋‹ค. ์ด๋Š” ์‹๊ฐ ํ”„๋กœํ•„, ํŠนํžˆ ์‹๊ฐ๋ฅ ์ด ์ด ๋ณ€์ˆ˜๋“ค์— ๋Œ€ํ•œ ํ•จ์ˆ˜๋กœ ํ‘œํ˜„๋  ์ˆ˜ ์žˆ์œผ๋ฉฐ, ์ด ๋ณ€์ˆ˜๋“ค์€ ์นจํˆฌ์„ฑ ์„ผ์„œ์ธ ๊ด‘ํ•™์  ๋ฐœ๊ด‘ ๋ถ„๊ด‘๋ฒ•์„ ํ†ตํ•ด ์ธก์ •๋  ์ˆ˜ ์žˆ๊ธฐ ๋•Œ๋ฌธ์ด๋‹ค. ๊ทธ ๋‹ค์Œ์—, ์ตœ์ ์˜ ๋‹ค๋ณ€์ˆ˜ ์‹œ์Šคํ…œ ์ •์˜๋ฅผ ์œ„ํ•ด ํŠน์ด์น˜ ๋ถ„์„๊ณผ ์ƒ๋Œ€์ด๋“๋ฐฐ์—ด์„ ์ด์šฉํ•˜์—ฌ ๊ฐ€์žฅ ํšจ๊ณผ์ ์œผ๋กœ ์ œ์–ด๋ฅผ ์ˆ˜ํ–‰ํ•  ์ˆ˜ ์žˆ๋Š” ์žฅ์น˜ ๋ณ€์ˆ˜ ์„ ์ •์ด ์ด๋ฃจ์–ด์กŒ๋‹ค. ์ด๋ฅผ ๋ฐ”ํƒ•์œผ๋กœ ๋‘ ๊ฐœ์˜ ๋ณ‘๋ ฌ๋กœ ์—ฐ๊ฒฐ๋œ ๋น„๋ก€์ ๋ถ„๋ฏธ๋ถ„์ œ์–ด๊ธฐ๋ฅผ ์„ค๊ณ„, ์•„๋ฅด๊ณค ํ”Œ๋ผ์ฆˆ๋งˆ ์ „์ž ๋ฐ€๋„์™€ ์ „์ž ์˜จ๋„์˜ ์ œ์–ด ์‹œ๋ฎฌ๋ ˆ์ด์…˜์„ ์ˆ˜ํ–‰ํ•˜์˜€๋‹ค. ํ•ด๋‹น ์‹œ๋ฎฌ๋ ˆ์ด์…˜์—์„œ ๋ณ€์ˆ˜๋“ค ๊ฐ„ ์ƒํ˜ธ ์ž‘์šฉ์ด ํ™•์—ฐํ•จ์„ ์ž…์ฆํ•˜์˜€์œผ๋ฉฐ ์ด๋ฅผ ํšจ๊ณผ์ ์œผ๋กœ ํ•ด๊ฒฐํ•˜๊ธฐ ์œ„ํ•ด ๋””์ปคํ”Œ๋Ÿฌ ์ œ์–ด๊ธฐ๊ฐ€ ๋น„๋ก€์ ๋ถ„๋ฏธ๋ถ„์ œ์–ด๊ธฐ์— ๊ฒฐํ•ฉ๋˜์—ˆ๋‹ค. ์ด ์ œ์–ด๊ธฐ๋Š” ์•„๋ฅด๊ณค ํ”Œ๋ผ์ฆˆ๋งˆ์˜ ์ „์ž ๋ฐ€๋„์™€ ์ „์ž ์˜จ๋„ ์ œ์–ด๋ฅผ ํ›Œ๋ฅญํ•˜๊ฒŒ ์ˆ˜ํ–‰ํ•จ์œผ๋กœ์จ ๋‹ค๋ณ€์ˆ˜ ํ”Œ๋ผ์ฆˆ๋งˆ ์‹œ์Šคํ…œ์˜ ์ œ์–ด ๊ฐ€๋Šฅ์„ฑ์„ ๋ถ„๋ช…ํ•˜๊ฒŒ ์ž…์ฆํ•˜์˜€๋‹ค. ๋‹ค๋ณ€์ˆ˜ ํ”Œ๋ผ์ฆˆ๋งˆ ์‹œ์Šคํ…œ์˜ ์ œ์–ด ๊ฐ€๋Šฅ์„ฑ์ด ์ž…์ฆ ๋์Œ์—๋„ ๋ถˆ๊ตฌํ•˜๊ณ , ์ด ์ œ์–ด ์ „๋žต์€ ๋น„๋ก€์ ๋ถ„๋ฏธ๋ถ„์ œ์–ด๊ธฐ์˜ ์ •๊ต์„ฑ ์ธก๋ฉด์—์„œ์˜ ํ•œ๊ณ„์™€ ๋””์ปคํ”Œ๋Ÿฌ ์ œ์–ด๊ธฐ์˜ ์‹œ์Šคํ…œ ๋ชจ๋ธ์— ๋Œ€ํ•œ ๋†’์€ ์˜์กด๋„ ํŠน์„ฑ์œผ๋กœ ์ธํ•œ ํ•œ๊ณ„๊ฐ€ ์กด์žฌํ•œ๋‹ค. ์‹œ์Šคํ…œ์ด ๋ณ€ํ•˜๋Š” ์ƒํ™ฉ์—์„œ๋„ ์„ฑ๋Šฅ์„ ์œ ์ง€ํ•˜๊ธฐ ์œ„ํ•ด์„  ๋”์šฑ ์ˆ˜์ค€ ๋†’์€ ์ œ์–ด ์ „๋žต์ด ์š”๊ตฌ๋˜๋ฉฐ, ๋ชจ๋ธ์˜ˆ์ธก์ œ์–ด๊ฐ€ ๊ทธ ๋Œ€์•ˆ์ด ๋  ์ˆ˜ ์žˆ๋‹ค. ๋ชจ๋ธ์˜ˆ์ธก์ œ์–ด๊ธฐ์˜ ์„ค๊ณ„๋Š” ์ œ์–ด์˜ ์ •๊ต์„ฑ์„ ๊ทน๋Œ€ํ™” ์‹œํ‚ค๊ธฐ ์œ„ํ•ด ๋ฒ ์ด์‹œ์•ˆ ์ตœ์ ํ™” ๊ธฐ๋ฒ•์„ ํ†ตํ•ด ์ด๋ฃจ์–ด์กŒ๋‹ค. ์ด ๋ชจ๋ธ์˜ˆ์ธก์ œ์–ด๊ธฐ๋Š” ์ธ์œ„์ ์ธ ์™ธ๋ž€์ด ์ ์šฉ๋˜์ง€ ์•Š์€ ์ˆœ์ˆ˜ ์•„๋ฅด๊ณค ํ”Œ๋ผ์ฆˆ๋งˆ ์‹œ์Šคํ…œ์—์„œ์˜ ์ „์ž ๋ฐ€๋„ ์ œ์–ด๋ฅผ ํ›Œ๋ฅญํ•˜๊ฒŒ ์ˆ˜ํ–‰ํ•จ์œผ๋กœ์จ ๊ทธ ์„ฑ๋Šฅ์„ ์ž…์ฆํ•˜์˜€๋‹ค. ํ•˜์ง€๋งŒ, ์‹œ์Šคํ…œ์ด ์‹œ๊ฐ„์— ๋”ฐ๋ผ ๋ณ€ํ•˜๋Š” ์ƒํ™ฉ์„ ๋ชจ์‚ฌํ•œ ์‹œ๋ฎฌ๋ ˆ์ด์…˜๊ณผ ์‚ฐ์†Œ ํ”Œ๋ผ์ฆˆ๋งˆ๊ฐ€ ์•„๋ฅด๊ณค ํ”Œ๋ผ์ฆˆ๋งˆ ์‹œ์Šคํ…œ์— ์ฃผ์ž…๋˜์–ด ์‹œ์Šคํ…œ ๋ณ€ํ™”๋ฅผ ์•ผ๊ธฐ์‹œํ‚ค๋Š” ์ƒํ™ฉ์—์„œ ์ˆ˜ํ–‰๋œ ์ œ์–ด ์‹คํ—˜์—์„œ ์ œ์–ด๊ธฐ์˜ ์„ฑ๋Šฅ์ด ํ™•์—ฐํžˆ ์•…ํ™”๋จ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค. ๋”ฐ๋ผ์„œ ์ด๋ฅผ ๊ทน๋ณตํ•  ์ˆ˜ ์žˆ๋Š” ๋”์šฑ ๋ฐœ์ „๋œ ์ œ์–ด ์ „๋žต์ด ์š”๊ตฌ๋˜์—ˆ๋‹ค. ์ ์‘ ์ œ์–ด ๊ธฐ๋ฒ•์€ ์‹œ์Šคํ…œ์—์„œ ์–ป์–ด์ง„ ์ •๋ณด๋ฅผ ์กฐ์ ˆ ๋ฉ”์ปค๋‹ˆ์ฆ˜ ๋ถ€๋ถ„์œผ๋กœ ๋ณด๋‚ด ์‹ค์‹œ๊ฐ„์œผ๋กœ ์ œ์–ด๊ธฐ์˜ ์ˆ˜์ • ์‚ฌํ•ญ์„ ๊ฒฐ์ •ํ•˜์—ฌ ์ด๋ฅผ ๋ฐ”ํƒ•์œผ๋กœ ์ œ์–ด๋ฅผ ์ˆ˜ํ–‰ํ•˜๋Š” ๊ธฐ๋ฒ•์ด๋‹ค. ๋ณธ ํ•™์œ„๋…ผ๋ฌธ์—์„œ๋Š” ๋Œ€ํ‘œ์ ์ธ ์ ์‘ ์ œ์–ด ์•Œ๊ณ ๋ฆฌ์ฆ˜์ธ ์ˆœํ™˜ํ˜• ์ตœ์†Œ์ž์Šน๋ฒ• ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ํ™œ์šฉํ•˜์˜€๋‹ค. ์ด ์•Œ๊ณ ๋ฆฌ์ฆ˜์— ์นผ๋งŒ ํ•„ํ„ฐ ํ•ด์„์„ ์ ‘๋ชฉ์‹œํ‚ด์— ๋”ฐ๋ผ, ํ”Œ๋ผ์ฆˆ๋งˆ ์‹๊ฐ ์žฅ์น˜๋กœ๋ถ€ํ„ฐ ๋น„๋กฏ๋˜๋Š” ์‹œ๊ฐ„ ์ง€์—ฐ์˜ ํšจ๊ณผ๋ฅผ ๊ณ ๋ คํ•  ์ˆ˜ ์žˆ๊ฒŒ ํ•˜์˜€๋‹ค. ์ด ์•Œ๊ณ ๋ฆฌ์ฆ˜์ด ํƒ‘์žฌ๋œ ์ˆœํ™˜ํ˜• ๋ชจ๋ธ ํŒŒ๋ผ๋ฏธํ„ฐ ์ถ”์ •๊ธฐ๋Š” ๋ฒ ์ด์‹œ์•ˆ ์ตœ์ ํ™” ๊ธฐ๋ฒ•์„ ํ†ตํ•ด ํŠœ๋‹๋˜์—ˆ๋‹ค. ์ˆœํ™˜ํ˜• ๋ชจ๋ธ ํŒŒ๋ผ๋ฏธํ„ฐ ์ถ”์ •๊ธฐ๊ฐ€ ์‹ค์‹œ๊ฐ„์œผ๋กœ ๊ฐ์ง€ํ•˜๋Š” ๋ชจ๋ธ ํŒŒ๋ผ๋ฏธํ„ฐ์˜ ๋ณ€ํ™”๋ฅผ ๋ชจ๋ธ์˜ˆ์ธก์ œ์–ด๊ธฐ์— ์ „๋‹ฌํ•˜๋ฉด ์ˆ˜์ •๋œ ๋ชจ๋ธ์„ ๊ธฐ๋ฐ˜์œผ๋กœ ์ œ์–ด๊ธฐ๋Š” ์ตœ์ ์˜ ์กฐ์ ˆ ๋ณ€์ˆ˜๋ฅผ ๊ณ„์‚ฐํ•œ๋‹ค. ์ด๋ ‡๊ฒŒ ์„ค๊ณ„๋œ ์ ์‘๋ชจ๋ธ์˜ˆ์ธก์ œ์–ด๊ธฐ๋Š” ์•ž์„œ ๋ชจ๋ธ์˜ˆ์ธก์ œ์–ด๊ธฐ๊ฐ€ ์ˆ˜ํ–‰ํ•œ ๊ฒƒ๊ณผ ๋™์ผํ•œ ์‹œ๋ฎฌ๋ ˆ์ด์…˜๊ณผ ์‹คํ—˜์„ ์ˆ˜ํ–‰ํ•˜์˜€๋‹ค. ๋ชจ๋ธ์˜ˆ์ธก์ œ์–ด๊ธฐ์™€ ๋‹ฌ๋ฆฌ ์ ์‘๋ชจ๋ธ์˜ˆ์ธก์ œ์–ด๊ธฐ๋Š” ์‹œ๊ฐ„์— ๋”ฐ๋ผ ์‹œ์Šคํ…œ์ด ๋ณ€ํ•˜๋Š” ์ƒํ™ฉ์—์„œ๋„ ํ›Œ๋ฅญํ•œ ์ œ์–ด๋ฅผ ์ˆ˜ํ–‰ํ•˜์˜€์œผ๋ฉฐ, ํ‰๊ท ์ ˆ๋Œ€์˜ค์ฐจ์œจ์„ ๊ธฐ์ค€์œผ๋กœ ํ–ˆ์„ ๋•Œ ๊ธฐ์กด์˜ ๋ชจ๋ธ์˜ˆ์ธก์ œ์–ด๊ธฐ๋ณด๋‹ค 24.7%์˜ ํ–ฅ์ƒ๋œ ์ œ์–ด ์„ฑ๋Šฅ์„ ๋ณด์—ฌ์ฃผ์—ˆ๋‹ค. ์ด ๊ฒฐ๊ณผ๋Š” ๋ณธ ํ•™์œ„๋…ผ๋ฌธ์—์„œ ์ œ์•ˆํ•˜๊ณ  ์žˆ๋Š” ์ ์‘๋ชจ๋ธ์˜ˆ์ธก์ œ์–ด๊ธฐ๊ฐ€ ์‹œ์Šคํ…œ์˜ ๋ณ€ํ™”๊ฐ€ ๋นˆ๋ฒˆํ•œ ํ”Œ๋ผ์ฆˆ๋งˆ ์‹œ์Šคํ…œ์—์„œ์˜ ์ œ์–ด์— ๋งค์šฐ ๊ฐ€์น˜ ์žˆ์Œ๊ณผ ๋”๋ถˆ์–ด ํ”Œ๋ผ์ฆˆ๋งˆ ์‹๊ฐ ์žฅ์น˜์— ์œ ํšจํ•œ ์ œ์–ด๊ธฐ๋ผ๋Š” ๊ฒƒ์„ ๋ฐ˜์ฆํ•œ๋‹ค. ์ด ๊ฒฐ๊ณผ๊ฐ€ ํ”Œ๋ผ์ฆˆ๋งˆ ๊ธฐ๋ฐ˜ ์‹œ์Šคํ…œ์„ ๋Œ€์ƒ์œผ๋กœ ํ•˜๋Š” ๋ชจ๋“  ์ œ์–ด ๊ณต์ •์˜ ๋ฐœ์ „์— ํฌ๊ฒŒ ์ด๋ฐ”์ง€ํ•  ๊ฒƒ์„ ๊ธฐ๋Œ€ํ•˜๋Š” ๋ฐ”์ด๋‹ค.Abstract i Contents v List of Figures viii List of Tables xii CHAPTER 1. Introduction 1 1.1. Research motivation 1 1.2. Research objectives 4 1.3. Description of the equipment used in this thesis 5 1.4. Outline of the thesis 9 CHAPTER 2. Design of Multi-Input Multi-Output Controller for Plasma-based System 10 2.1. Introduction 10 2.2. Theoretical backgrounds 13 2.2.1. Estimation of plasma variables from optical emission spectroscopy 13 2.2.2. The influence of oxygen in plasma etching reactor 16 2.2.3. Singular value decomposition and condition number 18 2.2.4. Relative gain array method 21 2.2.5. Multi-loop control system 23 2.3. MIMO control results in the Ar plasma system 31 2.3.1. Variable selection and pairing 31 2.3.2. Disturbance rejection control results for SISO systems 37 2.3.3. Simulation of multi-loop control scheme and decoupling control scheme 41 2.3.4. Set-point tracking control experiment of multi-loop controller with decoupler controllers 58 2.4. Concluding remarks 62 CHAPTER 3. Disturbance Rejection Control of Plasma Electron Density by Model Predictive Controller 64 3.1. Introduction 64 3.2. Model predictive control 68 3.2.1. Concept of model predictive control 68 3.2.2. Description of model predictive control algorithm 71 3.2.2.1. State estimation algorithm 71 3.2.2.2. Optimization algorithm 76 3.3. Design of model predictive controller for Ar plasma system 78 3.3.1. System identification of Ar plasma system 78 3.3.2. Optimal MPC weight parameters from integral squared error based Bayesian optimization 80 3.3.3. Experimental results of Ar plasma electron density control 84 3.4. Disturbance rejection control using model predictive controller 86 3.4.1. Development of time-varying system model for control simulation 86 3.4.2. Design of model predictive controller for disturbance rejection control 91 3.4.3. Experimental result of disturbance rejection control in Ar/O2 plasma system 101 3.5. Concluding remarks 104 CHAPTER 4. Design of Adaptive Model Predictive Controller for Plasma Etching Reactor 106 4.1. Introduction 106 4.2. Recursive model parameter estimation 112 4.2.1. Recursive least squares algorithm with forgetting factor 113 4.2.2. Recursive least squares algorithm with Kalman filter interpretation 116 4.3. Adaptive model predictive control algorithm 119 4.4. Time-varying system control using adaptive model predictive controller 123 4.4.1. Initial system identification (Scaling method) 123 4.4.2. Design of adaptive model predictive controller for time-varying system 125 4.4.3. Set-point tracking control results in drifted system 143 4.5. Concluding remarks 152 CHAPTER 5. Conclusion 154 5.1. Summary of contributions 154 5.2. Future work 157 Nomenclature 159 References 167 Abstract in Korean (๊ตญ๋ฌธ์ดˆ๋ก) 174Docto

    Neural Networks for Modeling and Control of Particle Accelerators

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    We describe some of the challenges of particle accelerator control, highlight recent advances in neural network techniques, discuss some promising avenues for incorporating neural networks into particle accelerator control systems, and describe a neural network-based control system that is being developed for resonance control of an RF electron gun at the Fermilab Accelerator Science and Technology (FAST) facility, including initial experimental results from a benchmark controller.Comment: 21 p

    Virtual metrology for plasma etch processes.

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    Plasma processes can present dicult control challenges due to time-varying dynamics and a lack of relevant and/or regular measurements. Virtual metrology (VM) is the use of mathematical models with accessible measurements from an operating process to estimate variables of interest. This thesis addresses the challenge of virtual metrology for plasma processes, with a particular focus on semiconductor plasma etch. Introductory material covering the essentials of plasma physics, plasma etching, plasma measurement techniques, and black-box modelling techniques is rst presented for readers not familiar with these subjects. A comprehensive literature review is then completed to detail the state of the art in modelling and VM research for plasma etch processes. To demonstrate the versatility of VM, a temperature monitoring system utilising a state-space model and Luenberger observer is designed for the variable specic impulse magnetoplasma rocket (VASIMR) engine, a plasma-based space propulsion system. The temperature monitoring system uses optical emission spectroscopy (OES) measurements from the VASIMR engine plasma to correct temperature estimates in the presence of modelling error and inaccurate initial conditions. Temperature estimates within 2% of the real values are achieved using this scheme. An extensive examination of the implementation of a wafer-to-wafer VM scheme to estimate plasma etch rate for an industrial plasma etch process is presented. The VM models estimate etch rate using measurements from the processing tool and a plasma impedance monitor (PIM). A selection of modelling techniques are considered for VM modelling, and Gaussian process regression (GPR) is applied for the rst time for VM of plasma etch rate. Models with global and local scope are compared, and modelling schemes that attempt to cater for the etch process dynamics are proposed. GPR-based windowed models produce the most accurate estimates, achieving mean absolute percentage errors (MAPEs) of approximately 1:15%. The consistency of the results presented suggests that this level of accuracy represents the best accuracy achievable for the plasma etch system at the current frequency of metrology. Finally, a real-time VM and model predictive control (MPC) scheme for control of plasma electron density in an industrial etch chamber is designed and tested. The VM scheme uses PIM measurements to estimate electron density in real time. A predictive functional control (PFC) scheme is implemented to cater for a time delay in the VM system. The controller achieves time constants of less than one second, no overshoot, and excellent disturbance rejection properties. The PFC scheme is further expanded by adapting the internal model in the controller in real time in response to changes in the process operating point

    Virtual metrology for plasma etch processes.

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    Plasma processes can present dicult control challenges due to time-varying dynamics and a lack of relevant and/or regular measurements. Virtual metrology (VM) is the use of mathematical models with accessible measurements from an operating process to estimate variables of interest. This thesis addresses the challenge of virtual metrology for plasma processes, with a particular focus on semiconductor plasma etch. Introductory material covering the essentials of plasma physics, plasma etching, plasma measurement techniques, and black-box modelling techniques is rst presented for readers not familiar with these subjects. A comprehensive literature review is then completed to detail the state of the art in modelling and VM research for plasma etch processes. To demonstrate the versatility of VM, a temperature monitoring system utilising a state-space model and Luenberger observer is designed for the variable specic impulse magnetoplasma rocket (VASIMR) engine, a plasma-based space propulsion system. The temperature monitoring system uses optical emission spectroscopy (OES) measurements from the VASIMR engine plasma to correct temperature estimates in the presence of modelling error and inaccurate initial conditions. Temperature estimates within 2% of the real values are achieved using this scheme. An extensive examination of the implementation of a wafer-to-wafer VM scheme to estimate plasma etch rate for an industrial plasma etch process is presented. The VM models estimate etch rate using measurements from the processing tool and a plasma impedance monitor (PIM). A selection of modelling techniques are considered for VM modelling, and Gaussian process regression (GPR) is applied for the rst time for VM of plasma etch rate. Models with global and local scope are compared, and modelling schemes that attempt to cater for the etch process dynamics are proposed. GPR-based windowed models produce the most accurate estimates, achieving mean absolute percentage errors (MAPEs) of approximately 1:15%. The consistency of the results presented suggests that this level of accuracy represents the best accuracy achievable for the plasma etch system at the current frequency of metrology. Finally, a real-time VM and model predictive control (MPC) scheme for control of plasma electron density in an industrial etch chamber is designed and tested. The VM scheme uses PIM measurements to estimate electron density in real time. A predictive functional control (PFC) scheme is implemented to cater for a time delay in the VM system. The controller achieves time constants of less than one second, no overshoot, and excellent disturbance rejection properties. The PFC scheme is further expanded by adapting the internal model in the controller in real time in response to changes in the process operating point

    Adaptive control and identification for on-line drug infusion in anaesthesia.

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    Anaesthesia is that part of the medical science profession which ensures that the patientโ€™s body is insensitive to pain and possibly other stimuli during surgical operations. It includes muscle relaxation (paralysis) and unconsciousness, both conditions being crucial for the operating surgeon. Maintaining a steady level of muscle relaxation as well as an acceptable depth of anaesthesia (unconsciousness), while keeping the dosage of administered drugs which induce those effects at a minimum level, have successfully been achieved using automatic control. Fixed gain controllers such as P, PI, and PID strategies can perform well when used in clinical therapy and under certain conditions but on the other hand can lead to poor performances because of the large variability between subjects. This is the reason which led to the consideration of adaptive control techniques which seemed to overcome such problems. Two control strategies falling into the above scheme and including the two newly developed techniques, i.e Proportional-Integral-Plus (PIP) control algorithm, and Generalized Predictive Control algorithm (GPC), are considered under extensive simulation studies using the muscle relaxation process associated with two drugs known as Pancuronium-Bromide and Atracurium. Both models exhibit severe non-linearities as well as time-varying dynamics and delays. Only the strategy corresponding to the GPC algorithm is retained for implementation on a 380Z disk-based microcomputer system, while the muscle relaxation process corresponding to either drugs is simulated on a VIDAC 336 analogue computer. The sensitivity of the algorithm is investigated when patient-to-patient parameter variability is evoked. The study is seen to provide the necessary basis for future clinical implementation of the scheme. Following the satisfactory results obtained under such a real-time environment, the self-adaptive GPC algorithm has been successfully applied in theatre to control Atracurium infusion on humans during surgery. This success later motivated further research work in which simultaneous control of muscle relaxation and anaesthesia (unconsciousness) was achieved. A good multivariable model has been derived and controlled via the multivariable version of the SISO GPC algorithm. The results obtained are very encouraging

    Innovative Surveillance and Process Control in Water Resource Recovery Facilities

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    Water Resource Recovery Facilities (WRRF), previously known as Wastewater Treatment Plants (WWTP), are getting increasingly complex, with the incorporation of sludge processing and resource recovery technologies. Along with maintaining a stringent effluent water quality standard, the focus is gradually shifting towards energy-efficient operations and recovery of resources. The new objectives of the WRRF demand an economically optimal operation of processes that are subjected to extreme variations in flowrate and composition at the influent. The application of online monitoring, process control, and automation in WRRF has already shown a steady increase in the past decade. However, the advanced model-based optimal control strategies, implemented in most process industries, are less common in WRRF. The complex nature of biological processes, the unavailability of simplified process models, and a lack of cost-effective surveillance infrastructure have often hindered the implementation of advanced control strategies in WRRF. The ambition of this research is to implement and validate cost-efficient monitoring alternatives and advanced control strategies for WRRF by fully utilizing the powerful Internet of Things (IoT) and data science tools. The first step towards implementing an advanced control strategy is to ensure the availability of surveillance infrastructure for monitoring nutrient compositions in WRRF processes. In Paper A, a soft sensor, based on Extended Kalman Filter, is developed for estimating water-quality parameters in a Sequential Batch MBBR process using reliable and inexpensive online sensors. The model used in the soft sensor combines the mechanistic understanding of the nutrient removal process with a statistical correlation between nutrient composition and easy-to-measure parameters. Paper B demonstrates the universality of the soft sensor through validation tests conducted in a Continuous Multistage MBBR pilot plant. The drift in soft-sensor estimation caused by a mismatch between the mathematical model and process behavior is studied in Paper B. The robustness of the soft sensor is assessed by observing estimated nutrient composition values for a period of three months. A systematic method to calibrate the measurement model and update model parameters using data from periodic lab measurements are discussed in Paper B. The term SCADA has been ubiquitous while mentioning online monitoring and control strategy deployment in WRRFs. The present digital world of affordable communication hardware, compact single board processors, and high computational power presents several options for remote monitoring and deployment of soft sensors. In Paper C, a cost-effective IoT strategy is developed by using an open-source programming language and inexpensive hardware. The functionalities of the IoT infrastructure are demonstrated by using it to deploy a soft sensor script in the ContinuousMultistage MBBR pilot plant. A cost-comparison between the commercially available alternatives presented in Paper A and the open-source IoT strategy in Paper B and Paper C highlights the benefits of the new monitoring infrastructure. Lack of reliable control models have often been the cause for the poor performance of advanced control strategies, such as Model Predictive Controls (MPC) when implemented to complex biological nutrient removal processes. Paper D attempts to overcome the inadequacies of the linear prediction model by combining a recursive model parameter estimator with the linear MPC. The new MPC variant, called the adaptive MPC (AMPC), reduces the dependency of MPC on the accuracy of its prediction model. The performance of the AMPC is compared with that of a linear MPC, nonlinear MPC, and the traditional proportional-integral cascade control through simulator-based evaluations conducted on the Benchmark Simulator platform(BSM2). The advantages of AMPC compared to its counterparts, in terms of reducing the aeration energy, curtailing the number of effluent ammonia violations, and the use of computational resources, are highlighted in Paper D. The complex interdependencies between different processes in a WRRF pose a significant challenge in defining constant reference points for WRRFs operations. A strategy that decides control outputs based on economic parameters rather than maintaining a fixed reference set-point is introduced in Paper E. The model-based control strategy presented in Paper D is further improved by including economic parameters in the MPCโ€™s objective function. The control strategy known as Economic MPC (EMPC) is implemented for optimal dosage of magnesium hydroxide in a struvite recovery unit installed in a WRRF. A comparative study performed on the BSM2 platform demonstrates a significant improvement in overall profitability for the EMPC when compared to a constant or a feed-forward flow proportional control strategy. The resilience of the EMPC strategy to variations in the market price of struvite is also presented in Paper E. A combination of cost-effective monitoring infrastructure and advanced control strategies using advanced IoTs and data science tools have been documented to overcome some of the critical problems encountered in WRRFs. The overall improvement in process efficiency, reduction in operating costs, an increase in resource recovery, and a substantial reduction in the price of online monitoring infrastructure contribute to the overall aim of transitioning WRRFs to a self-sustaining facility capable of generating value-added products.Water Resource Recovery Facilities (WRRF), tidligere kjent som avlรธpsrenseanlegg (WWTP), blir stadig mer komplekse ettersom flere prosess steg tillegges anleggene i form av slambehandling og ressursgjenvinningsteknologi. Foruten hovedmรฅlet om รฅ imรธtekomme strenge avlรธpsvannskvalitetskrav, har anleggenes fokus gradvis skiftet mot energieffektiv drift og gjenvinning av ressurser. Slike nye mรฅl krever รธkonomisk optimal drift av prosesser som er utsatt for ekstreme variasjoner i volum og sammensetning av tillรธp. Bruk av online overvรฅking, prosesskontroll og automatisering i WRRF har jevnt รธkt det siste tiรฅret. Likevel er avanserte modellbaserte kontrollstrategier for optimalisering ikke vanlig i WRRF, i motsetning til de fleste prosessindustrier. Komplekse forhold i biologiske prosesser, mangel pรฅ tilgang til pรฅlitelige prosessmodeller og mangel pรฅ kostnadseffektiv overvรฅkingsinfrastruktur har ofte hindret implementeringen av avanserte kontrollstrategier i WRRF. Ambisjonen med denne avhandlingen er รฅ implementere og validere kostnadseffektive overvรฅkingsalternativer og avanserte kontrollstrategier somutnytter kraftige Internet of Things (IoT) og datavitenskapelige verktรธy i WRRF sammenheng. Det fรธrste steget mot implementering av en avansert kontrollstrategi er รฅ sรธrge for tilgjengelighet av overvรฅkingsinfrastruktur for mรฅling av nรฆringsstoffer i WRRF-prosesser. Paper A demonstrerer en virtuell sensor basert pรฅ et utvidet Kalman filter, utviklet for รฅ estimere vannkvalitetsparametere i en sekvensiell batch MBBR prosess ved hjelp av pรฅlitelige og rimelige online sensorer. Modellen som brukes i den virtuelle sensoren kombinerer en mekanistisk forstรฅelse av prosessen for fjerning av nรฆringsstoffer fra avlรธpsvann med et statistisk sammenheng mellom nรฆringsstoffsammensetning i avlรธpsvann og parametere som er enkle รฅ mรฅle. Paper B demonstrerer det universale bruksaspektet til den virtuelle sensoren gjennom valideringstester utfรธrt i et kontinuerlig flertrinns MBBR pilotanlegg. Feilene i sensorens estimering forรฅrsaket av uoverensstemmelse mellom den matematiske modellen og prosesseatferden er undersรธkt i Paper B. Robustheten til den virtuelle sensoren ble vurdert ved รฅ observere estimerte nรฆringssammensetningsverdier i en periode pรฅ tre mรฅneder. En systematisk metode for รฅ kalibrere mรฅlemodellen og oppdatere modellparametere ved hjelp av data fra periodiske laboratoriemรฅlinger er diskutert i Paper B. Begrepet SCADA har alltid vรฆrt til stede nรฅr online overvรฅking og kontrollstrategi innen WRRF er nevnt. Den nรฅvรฆrende digitale verdenen med god tilgjengelighet av rimelig kommunikasjonsmaskinvare, kompakte enkeltkortprosessorer og hรธy beregningskraft presenterer flere muligheter for fjernovervรฅking og implementering av virtuelle sensorer. Paper C viser til utvikling av en kostnadseffektiv IoT-strategi ved hjelp av et programmeringssprรฅk med รฅpen kildekode og rimelig maskinvare. Funksjonalitetene i IoT-infrastruktur demonstreres gjennom implementering av et virtuelt sensorprogram i et kontinuerlig flertrinns MBBR pilotanlegg. En kostnadssammenligning mellom de kommersielt tilgjengelige alternativene som presenteres i Paper A og รฅpen kildekode-IoT-strategi i Paper B og Paper C fremhever fordelene med den nye overvรฅkingsinfrastrukturen. Mangel pรฅ pรฅlitelige kontrollmodeller har ofte vรฆrt รฅrsaken til svake resultater i avanserte kontrollstrategier, som for eksempel Model Predictive Control (MPC) nรฅr de implementeres i komplekse biologiske prosesser for fjerning av nรฆringsstoffer. Paper D prรธver รฅ lรธse manglene i MPC ved รฅ kombinere en rekursiv modellparameterestimator med lineรฆr MPC. Den nye MPC-varianten, kalt Adaptiv MPC (AMPC), reduserer MPCs avhengighet av nรธyaktigheten i prediksjonsmodellen. Ytelsen til AMPC sammenlignes med ytelsen til en lineรฆr MPC, ikke-lineรฆr MPC og tradisjonell proportionalintegral kaskadekontroll gjennom simulatorbaserte evalueringer utfรธrt pรฅ Benchmark Simulator plattformen (BSM2). Fordelene med AMPC sammenlignet med de andre kontrollstrategiene er fremhevet i Paper D og demonstreres i sammenheng redusering av energibruk ved lufting i luftebasseng, samt redusering i antall brudd pรฅ utslippskrav for ammoniakk og bruk av beregningsressurser. De komplekse avhengighetene mellom forskjellige prosesser i en WRRF utgjรธr en betydelig utfordring nรฅr man skal definere konstante referansepunkter for WRRF under drift. En strategi som bestemmer kontrollsignaler basert pรฅ รธkonomiske parametere i stedet for รฅ opprettholde et fast referansesettpunkt introduseres i Paper E. Den modellbaserte kontrollstrategien fra PaperDforbedres ytterligere ved รฅ inkludere รธkonomiske parametere iMPCs objektiv funksjon. Denne kontrollstrategien kalles Economic MPC (EMPC) og er implementert for optimal dosering av magnesiumhydroksid i en struvit utvinningsenhet installert i en WRRF. En sammenligningsstudie utfรธrt pรฅ BSM2 plattformen viste en betydelig forbedring i den totale lรธnnsomheten ved bruk av EMPC sammenlignet med en konstant eller en flow proportional kontrollstrategi. Robustheten til EMPC-strategien for variasjoner i markedsprisen pรฅ struvit er ogsรฅ demonstrert i Paper E. En kombinasjon av kostnadseffektiv overvรฅkingsinfrastruktur og avanserte kontrollstrategier ved hjelp av avansert IoT og datavitenskapelige verktรธy er brukt for รฅ lรธse flere kritiske utfordringer i WRRF. Den samlede forbedringen i prosesseffektivitet, reduksjon i operasjonskostnader, รธkt ressursgjenvinning og en betydelig reduksjon i pris for online overvรฅkningsinfrastruktur bidrar til det overordnede mรฅlet om รฅ gรฅ over til bรฆrekraftige WRRF som er i stand til รฅ generere verdiskapende produkter.DOSCON A

    Closed-Loop Control of Anaesthetic Effect

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    Archivo disponible en la web de la revista, Open Access, en la siguiente URL: https://www.intechopen.com/books/pharmacology/closed-loop-control-of-anesthetic-effect Se puede referenciar de la siguiente manera: Santiago Torres, Juan A. Mรฉndez, Hรฉctor Reboso, Josรฉ A. Reboso and Ana Leรณn (2012). Closed-Loop Control of Anaesthetic Effect, Pharmacology, Dr. Luca Gallelli (Ed.), InTech, DOI: 10.5772/37609. Available from: https://www.intechopen.com/books/pharmacology/closed-loop-control-of-anesthet

    Nonlinear identification and control of muscle relaxant dynamics.

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    The work reported in this thesis comprised two major parts which are: 1) Off-line nonlinear identification of muscle relaxant dynamics, 2) Simulation-based design of a variety of controllers (ranging from classical PID to nonlinear self-tuners) for the closed-loop control of muscle relaxation. Relaxant drugs namely, Vecuronium and Atracurium are considered throughout. Off-line identification studies, using two special nonlinear identification packages (Nonlinear Identification package and Nonlinear Orthogonal Identification package), were carried out to determine nonlinear difference equation models (NARMAX) that best fit (in the least squares sense) recorded data from trials on humans and dogs for each drug. After validation, these models were assumed to represent, in a nonlinear polynomial form, the muscle relaxant drugs pharmacology. Two different approaches were explored for determining the physiological structure of both relaxant drugs: a) The drug model to comprise a pharmacokinetics part to represent the drug distribution, and pharmacodynamics which are often modelled by using the well known Hill equation. b) A cross-correlation approach based on Volterra series. With the relaxant dynamics structure thus fixed, the work proceeded to the control phase. Simple three-term PID controllers were first designed with their parameters being optimised, off-line, using the Simplex method. The non-adaptive nature of this class of controllers makes their robustness open to question when the system parameters for which they have been optimised change. Hence adaptive controllers in the form of linear and nonlinear generalised minimum variance, self-tuners, generalised predictive and nonlinear k-step ahead predictive controllers were also considered. All these latter control approaches are shown to be satisfactory, in terms of transient and steady state performance
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