Ensuring Dynamic Stability of the Automatic Control System for Glass Thickness in the Presence of Transport Delay
Abstract Generated abstract
This paper addresses the stabilization of sheet glass thickness in vertical drawing when transport delay between formation and measurement can undermine control-system dynamics. It reviews the limitations of predictive and Smith-type schemes that require a technically complex model with automatically variable delay, then presents a control structure that uses the transport delay inherent in the object to model the delay in the predictive device. Under equality of the delay-free transfer functions of the object and its model, the closed-loop transfer function contains no delay term in the denominator, so the variable transport delay does not affect stability. The proposed scheme was adopted as the basis for designing an automatic glass-thickness control system for the Anzhero-Sudzhensk Glass Plant.
Full Text
ENSURING DYNAMIC STABILITY OF THE AUTOMATIC CONTROL SYSTEM FOR GLASS THICKNESS IN THE PRESENCE OF TRANSPORT DELAY
V. A. BEINAROVICH, L. K. BEZRODNY
(Presented by the Scientific and Technical Seminar of the Research Institute of AEM)
One of the main technical-and-economic indicators in the production of sheet glass is its thickness. Fluctuations in glass thickness arising during the drawing process as a result of nonconstancy of viscosity, the level of the glass melt, the temperature in the forming zone, and other factors [1, 2] cause deterioration of glass quality and overconsumption of glass melt. Studies [3] have shown the possibility of stabilizing the thickness of a glass ribbon produced by the vertical drawing method by automatically controlling its drawing speed with the use of a predictive model in the controller [4]. However, the practical value of the proposed automatic control system, as well as of an automatic control system with a Smith predictor [5], is small, since in order to compensate for the influence of transport delay on the dynamic stability of the automatic control system [4, 5], the system must contain a technically complex correcting device—a model of a link with variable transport delay. In this case, according to the conditions for preserving the specified dynamic properties and stability margins [6], the model must have a corresponding automatic adjustment of the delay as a function of the drawing speed of the glass ribbon and the distance between the surface of the glass melt in the drawing chamber and the installation site of the glass-ribbon thickness sensor, which additionally complicates and increases the cost of the model.
Fig. 1.
The Smith [5] scheme is small in value, since in order to compensate for the influence of transport delay on the dynamic stability of the automatic control system [4, 5], the system must contain a technically complex correcting device—a model of a link with variable transport delay. In this case, according to the conditions for preserving the specified dynamic properties and stability margins [6], the model must have a corresponding automatic adjustment of the delay as a function of the drawing speed of the glass ribbon and the distance between the surface of the glass melt in the drawing chamber and the installation site of the glass-ribbon thickness sensor, which additionally complicates and increases the cost of the model.
In [7] an original method was proposed for using the transport delay present in the object to model the delay in the predictive device of the automatic control system. The block diagram of the automatic control system for glass thickness that implements this method is presented in Fig. 1. Under the condition that the transfer functions of the object model \(W_{\text{mo}}(p)\) and of the controlled object \(W_0(p)\) are equal, without taking transport delay into account, the transfer function of the closed-loop automatic control system with respect to the set-point action takes the form
\[ W(p)=\frac{\delta(p)}{\delta_0(p)} = -\frac{W_{\text{uy}}(p)\cdot W_0(p)\cdot e^{-p\tau_0}} {1+W_{\text{uy}}(p)\cdot W_{\text{mo}}(p)}, \tag{1} \]
where \(W_{\text{uy}}(p)\), \(e^{-p\tau_0}\) are the transfer functions of the control device and of the transport-delay element of the controlled object;
\(\delta_0\), \(\delta\) are the specified and actual values of the thickness of the glass ribbon.
The minus sign before the transfer function of the automatic control system (1) reflects the inversely proportional dependence between the drawing speed of the glass ribbon \(v\) and the thickness \(\delta\) of the glass obtained. In the denominator of expression (1) there is no term characterizing the delay. Therefore the variable transport delay present in the object has no effect on the stability of the automatic control system. The stability of a system with transfer function (1) can readily be ensured by known correction methods.
The block diagram considered was adopted as the basis for designing an automatic control system for the thickness of sheet glass for the Anzhero-Sudzhensk Glass Plant.
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