Research articleHeating-up control with delay-free output prediction for industrial jacketed reactors based on step response identification
Introduction
Heating-up control is an important operation for industrial jacketed reactors widely used for chemical material mixture, pharmaceutical crystallization, and biological fermentation. Owing to that the exchange of thermal energy is limited by the heat transfer surface between the jacket and the reactor, the heating-up process usually has long time delay and slow dynamics in response to the heating power [1]. Generally, the heating-up process of a jacketed reactor can be viewed as a typical integrating process with time delay, since the reactor temperature will remain unchanged for certain time after the electrical heater is fully turned on, and then rise up continuously rather than reaching a steady state. The main control challenge for such a process is to track the set-point temperature profile as fast as possible while avoiding overheating (related to temperature overshoot), and then maintain the set-point temperature for operation against load disturbance such as feeding raw materials with a lower temperature, heat radiation from the reactor, and ambient air convection. It has been widely recognized that slow dynamics and long time delay of thermal processes bring difficulties to the temperature control design [2], [3], [4], [5], in particular for suppressing overshoot in the set-point tracking and ‘long tail’ in the sluggish output response to load disturbance [6].
Different control strategies have been developed to improve control performance for integrating processes with time delay in the literature. Based on the classical unity feedback control structure, improved proportional–integral–derivative (PID) tuning methods can be found in the recent papers [7], [8], [9], [10], [11]. The achievable control performance by tuning a PID controller for an integrating process was analyzed in the paper [12]. To overcome the water-bed effect involved with a unity feedback control structure for the set-point tracking and load disturbance rejection for an integrating process, two-degree-of-freedom (2DOF) control schemes have been developed in the references, e.g., the internal model control (IMC) based 2DOF control methods based on using different controller forms including PID for implementation [13], [14], [15], [16], the time compensator based 2DOF control designs for integrating processes with time delay [17], [18], and the discrete-time predictor based 2DOF control methods for implementation in sampled control systems [19], [20], [21], [22], [23]. To deal with the input constraints related to the temperature control of jacketed reactors, it was suggested to divide such a heating-up process into a series of operating phases for piecewise modeling [24], such that a gain scheduling control scheme based on using a simple PD controller could be designed for implementation. This control strategy, however, required a prior knowledge of the process operation that may not be available in practical applications.
Note that although a number of model-based control methods as aforementioned had been developed to improve the control performance for various temperature control systems, only a few references presented model identification methods for integrating processes with time delay [25]. Compared to the identification of a stable process, the input excitation for performing an identification test on an integrating process like the heating-up operation must be limited to a finite time in order to avoid the output response moving beyond the permitted operational range in practice. Closed-loop step or relay tests had been mainly used in the existing references to establish a low-order integrating type process model with time delay such as the first-order-plus-dead-time (FOPDT) or second-order-plus-dead-time (SOPDT) model [26], [27], [28], [29], [30], [31]. In fact, these closed-loop identification methods are confined to describe the process response characteristics around the set-point value, due to the closed-loop feedback mechanism. Few Refs. [5], [32] explored open-loop step response identification algorithms based on a finite number of output response data under a step change of the set-point.
To facilitate identifying the fundamental dynamics of a jacketed reactor during the heating-up operation, an open-loop step response identification method is proposed in this paper to establish an integrating type process model with time delay, which further extends the step response identification approach developed in the Refs. [33], [34] purely for open-loop stable processes. By introducing a damping factor to the step response, a finite number of the observed step response data can be effectively used for the frequency response estimation and model fitting, therefore alleviating a practical limit of the output range to an open-loop step test. Based on the identified model, a delay-free output prediction based 2DOF control scheme is proposed. The delay-free output prediction is established by designing two stable filters based on the process input and output measurement, as inspired by the recently developed predictor designs in discrete-time domain for sampled systems with input delay [21], [22]. Both controllers are analytically designed in frequency domain by proposing the desired transfer functions for the set-point tracking and load disturbance rejection, respectively. There is a single adjustable parameter in each controller that may be monotonically tuned to obtain the desired control performance.
For clarity, the paper is organized as follows. Section 2 presents a step response identification method for modeling the fundamental heating-up dynamics of a jacketed reactor, along with two illustrative examples. In Section 3, a delay-free output prediction based 2DOF control scheme is presented for the heating-up operation together with the robust stability analysis, and two benchmark examples from the literature are used to demonstrate the control performance. Experimental tests on a 4-liter jacketed reactor for pharmaceutical crystallization are performed in Section 4. Finally, some conclusions are drawn in Section 5.
Section snippets
Identification of heating-up dynamics for jacketed reactors
Consider a temperature control system for a jacketed reactor shown in Fig. 1, where the temperature control system consists of a heating circulator filled with the thermal conduction medium (e.g., ethylene glycol mixed with distiller water), an electrical heater regulated via a zero-crossing solid state relay (SSR) with pulse-width modulation (PWM) and commanded by a programmable logic controller (PLC), and a thermometer (e.g., Pt100) for measuring the solution temperature in the reactor.
It is
Control system design
For the heating-up process of a jacketed reactor, overshoot in the output response is inevitably provoked by the classical unity feedback control structure, unless the set-point tracking speed is tuned very slow [1], which is indeed undesired for system operation in engineering applications. Besides, there are practical constraints for control implementation, such as regulating the heating power is limited in a range of [0, 100]% with respect to the nominal power of an electrical heater, and no
Experimental results
Consider the temperature control system for a 4-liter pharmaceutical crystallization reactor containing 2-liter aqueous solution, as shown in Fig. 1. The temperature control system consists of a 7-liter heating circulator filled with ethylene glycol and distilled water in proportion of 2:3, an electrical heater with a capacity of 2000 W regulated via an SSR and a PWM, a PT100 thermometer, a PLC made by Siemens company, and a 64-bit data acquisition card (AT-MIO-64X) of National Instruments (NI)
Conclusions
For the heating-up control of industrial jacketed reactors, a step response identification method has been proposed to establish an integrating type process model with time delay for describing fundamental dynamics of the heating-up response, therefore extending the developed step response identification methods [33], [34] purely for stable processes with time delay. It has been demonstrated that different choices of the damping factor in a proper range could give similar identification
Acknowledgement
This work was supported in part by the NSF China Grants 61633006 and 61473054, and the Fundamental Research Funds for the Central Universities of China .
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