As a typical complex industrial process [
1,
2], the dividing-wall distillation column (DWDC) is famous for its excellent energy-saving and investment-reducing capacities [
3,
4,
5]. However, it is very hard to achieve its stable operation and strict product quality control due to its characteristics of high nonlinearity and large time delay. This control problem constrains greatly the application of the DWDC in chemical industries [
6] and reminds us of the importance of studying the control of the DWDC.
Focusing on the control of the DWDC, a wide range of control methods have been studied, including but not limited to direct composition control [
7,
8,
9,
10], composition-temperature cascade control [
11,
12], and temperature inferential control [
13,
14,
15,
16]. Among them, temperature inferential control has the largest application potential in the chemical industry because of its obvious superiorities in dynamic characteristics and equipment investment. The only pity is that temperature inferential control schemes may give rise to large steady-state deviations in the product purities to be maintained due to unpredictable pressure variations within the DWDC. For the purpose of reducing the steady-state deviations in the product purities to be maintained substantially, many studies have been conducted in recent years to give various effective temperature inferential control schemes. For instance, Ling and Luyben gave a temperature difference control (TDC) scheme that involves four temperature difference control loops for controlling the Petlyuk DWDC [
17]. Because the effects of pressure variations on the two stage temperatures that form the temperature difference are similar and can offset each other to a certain degree, the estimation accuracy of the temperature difference is less influenced by pressure variations. Therefore, the TDC scheme could achieve stricter product quality control than the conventional temperature control scheme. Wu et al. proposed a double temperature difference control (DTDC) scheme for the control of the Petlyuk DWDC by employing a double temperature difference to estimate the maintained product purity in each control loop [
18]. Because the effects of pressure variations on the two temperature differences that form the double temperature difference are similar and can be offset each other, the performance of the DTDC scheme was further improved as compared with the TDC scheme. Not only were the steady-state errors in the maintained product purities obviously reduced, but also the capability of rejecting feed disturbances was improved. Subsequently, Yuan et al. found that it is possible to further increase the estimation accuracy of the double temperature difference to the maintained product purity by carefully coordinating the relationship between the two temperature differences that form the double temperature difference, and developed a new derivation method of the DTDC scheme [
19]. According to their dynamic simulation results, the DTDC scheme derived by the new method could result in smaller steady-state errors in the product purities to be maintained as compared with the DTDC scheme derived by the conventional method. Furthermore, Pan et al. developed a pressure-compensated temperature control loop to enhance the control of the lower sidestream product for a Kaibel DWDC [
20]. For this pressure-compensated temperature control loop, pressure and temperature of a stage, including primarily binary mixture, were first measured, and the composition of this stage was then inferred to be used as the controlled variable, relying on an equation describing the relationship among the temperature, the pressure, and composition. Although this pressure-compensated temperature control loop is effective, its principle is too complicated to be popular.
Based on the above analysis, we can clearly find that the key to improving the steady-state performance of the temperature inferential control scheme lies in employing appropriate pressure compensation methods. In the current work, we will propose a kind of novel product quality estimator (PQE). It can suppress the adverse effect of pressure variations and provide a more accurate estimation of the product purity to be maintained according to the stage temperatures measured. In the remainder of this article, the structure of the proposed PQE and its design method are firstly elaborated in
Section 2. In terms of two DWDCs, including one Petlyuk DWDC separating an ethanol (E)/propanol (P)/butanol (B) ternary mixture (EPB Petlyuk DWDC) and one Kaibel DWDC separating methanol (M)/E/P/B quaternary mixture (MEPB Kaibel DWDC), comparisons between the DTDC scheme derived by the new method (its steady-state and dynamic performances are more excellent than those of the other temperature difference control schemes, and thus it is employed here as a comparison) and the temperature inferential control scheme using the PQE (TC-PQE) are conducted to assess the effectiveness of the PQE in
Section 3 and
Section 4. An objective evaluation of the proposed PQE is provided in
Section 5. Some conclusions are briefly given in
Section 6.