Jyh-Cheng Jeng

A direct method for multi-loop PI/PID controller design

Difficulties caused by the interactions are always encountered in the design of multi-loop control systems for MIMO processes. To overcome the difficulties, a multi-loop system is decomposed into a number of equivalent single loops for design. For each equivalent single loop, an effective open-loop process (EOP) is formulated without prior knowledge of controller dynamics in other loops, and, hence, controller can be designed directly and independently. Based on the derived EOPs, a model-based method aims at having reasonable gain margins (e.g. 52) and phase margins (e.g. � 60 � ) are presented to derive multi-loop PI/PID controllers. This proposed method is formulated in details for the EOPs of 2-loop systems. Extension to higher dimensional systems needs further simplification and is illustrated with formulation for 3-loop systems. Simulation results show that this presented method is effective for square MIMO processes, especially, for low dimensional ones. # 2003 Elsevier Ltd. All rights reserved.

Multiple sensor fault diagnosis for dynamic processes

Modern industrial plants are usually large scaled and contain a great amount of sensors. Sensor fault diagnosis is crucial and necessary to process safety and optimal operation. This paper proposes a systematic approach to detect, isolate and identify multiple sensor faults for multivariate dynamic systems. The current work first defines deviation vectors for sensor observations, and further defines and derives the basic sensor fault matrix (BSFM), consisting of the normalized basic fault vectors, by several different methods. By projecting a process deviation vector to the space spanned by BSFM, this research uses a vector with the resulted weights on each direction for multiple sensor fault diagnosis. This study also proposes a novel monitoring index and derives corresponding sensor fault detectability. The study also utilizes that vector to isolate and identify multiple sensor faults, and discusses the isolatability and identifiability. Simulation examples and comparison with two conventional PCA-based contribution plots are presented to demonstrate the effectiveness of the proposed methodology.

Disturbance-rejection-based tuning of proportional-integral-derivative controllers by exploiting closed-loop plant data.

A systematic data-based design method for tuning proportional-integral-derivative (PID) controllers for disturbance attenuation is proposed. In this method, a set of closed-loop plant data are directly exploited without using a process model. PID controller parameters for a control system that behaves as closely as possible to the reference model for disturbance rejection are derived. Two algorithms are developed to calculate the PID parameters. One algorithm determines the optimal time delay in the reference model by solving an optimization problem, whereas the other algorithm avoids the nonlinear optimization by using a simple approximation for the time delay term, enabling derivation of analytical PID tuning formulas. Because plant data integrals are used in the regression equations for calculating PID parameters, the two proposed algorithms are robust against measurement noises. Moreover, the controller tuning involves an adjustable design parameter that enables the user to achieve a trade-off between performance and robustness. Because of its closed-loop tuning capability, the proposed method can be applied online to improve (retune) existing underperforming controllers for stable, integrating, and unstable plants. Simulation examples covering a wide variety of process dynamics, including two examples related to reactor systems, are presented to demonstrate the effectiveness of the proposed tuning method.

Control strategies for thermal budget and temperature uniformity in spike rapid thermal processing systems

Abstract Single wafer rapid thermal processing (RTP) is widely used in semiconductor manufacturing. A precisely applied thermal budget during RTP is crucial and relies on the temperature control of the wafer. However, temperature control in the RTP system with a spike-shaped temperature profile is a challenging task, and achieving perfect servo control is almost impossible because of the high temperature ramp-up/down rate and substantial nonlinearity of the process. This paper presents a novel method of control system design to provide a precise thermal budget in the spike RTP system. By tuning controller parameters and designing the set-point profile, the method targets thermal budget indices instead of temperature servo control. A nonlinear control strategy is proposed based on modeling the RTP system as a nonlinear Wiener model. Furthermore, a multivariable control structure is considered to maintain the temperature uniformity within the wafer. The simulation results show the effectiveness of the proposed control strategy and provide helpful guidelines for the design of a multivariable control configuration to achieve superior wafer temperature uniformity.

Context-based State Estimation in Semiconductor Manufacturing: Reference Path Based State Transformation Approach

There are many possible factors in semiconductor manufacturing processes such as metrology tool bias, product type, or chamber that may induce disturbance to the process output. To account for all these types, a context-based model is often used. The most important feature of a context-based system is rank deficiency, and therefore we propose a method that unbiasedly estimates the relative status of each context and process output by state transformation. The transformed states are straightforward and physically meaningful. Furthermore, a solution of planning paths with a guarantee of output performance is also investigated. The other application of particle count estimation for data from a real fab is also demonstrated.

Data-based design of centralized PID controllers for decoupling control of multivariable processes

This paper presents a data-based design method of decoupling PID controllers for multivariable processes. The controller design directly exploits experimental process data without identifying process models. By employing the virtual reference approach, a centralized controller that achieves ideal decoupling control is first synthesized. Then, each controller element is approximated to PID structure. The control design depends on the reference model that is optimally specified according to the attainment of the reference model and the effectiveness of decoupling. Because the controller design is applicable to closed-loop data, it is preferable in industrial applications and the method can be used to improve existing underperforming controllers. Simulation studies demonstrate the effectiveness of the proposed design methodology.

Extended VRFT Method for Controller Design of Nonlinear Systems Based on Block-Oriented Model Structures

Abstract This paper presents a novel data-based controller design for nonlinear systems based on the VRFT design framework and block-oriented modeling. Identification of a complete dynamic model of the nonlinear system is not required, whereas only the static nonlinearity has to be estimated. Moreover, the nonlinearity estimation and the controller design are performed simultaneously without the needs of iterative procedures or nonlinear optimization. Simulation studies of a distillation column and a pH neutralization process confirms the effectiveness of the proposed design method.

Controller Design for Nonlinear Hammerstein and Wiener Systems Based on VRFT Method

Abstract This paper presents a novel data-based controller design for nonlinear Hammerstein and Wiener systems based on the VRFT design framework. In the proposed method, identification of a complete dynamic model of the nonlinear system is not required, whereas only the static nonlinearity has to be estimated. Furthermore, the nonlinearity estimation and the controller design are performed simultaneously without the needs of iterative procedures or nonlinear optimization. Simulation study of a pH neutralization process confirms the effectiveness of the proposed controller design method.

Identification and Controller Tuning of Cascade Control Systems Based on Closed-Loop Step Responses

Abstract This paper presents a new automatic tuning method for cascade control systems based on a single closed-loop step test. The proposed method identifies the required process information with the help of B-spline series expansions for the step responses. The two PID controllers are then tuned using an internal model control (IMC) approach. The secondary controller is designed for enhanced disturbance rejection, and the primary controller is designed, without requiring an additional test, based on an identified process model that accurately accounts for the inner loop dynamics. The desired levels of system robustness explicitly guide the selection of the IMC tuning parameters. The proposed method is robust to measurement noises because of the filtering property of the B-splines, and can provide satisfactory control performance. Simulation examples confirm the effectiveness of the proposed method.

NONPARAMETRIC METHOD FOR IDENTIFICATION OF MIMO HAMMERSTEIN MODELS

Abstract A new nonparametric approach to identify multivariable Hammerstein models is presented in this paper. The linear dynamic subsystem is identified and represented by its finite impulse response (FIR) model, and, the static nonlinearity is identified and represented as an MIMO input-output mapping. By specially designed test signals, the estimation of FIRs for multivariable linear subsystems can be conducted under a SISO framework and can be decoupled from the identification of the static nonlinearity. Due to the nonparametric nature, the representation of MIMO Hammerstein model may not be unique. By making uses of this fact, several parameters can be adjusted to shape the model for achieving engineers requirement. These above-mentioned representations can be used to obtain an exact process model or an apparent model suitable for control design.