Dual-loop SISO controller development for food-extrusion

In order to better understand and motivate students to the needs of dynamic modeling and multivariable (MVSISO) design consideration, the case-study of a twinscrew food extruder provides a real-life example with all the requisite components necessary for unit operations management. The study provides a two-input, two-output system able to be simulated via Simulink model that requires knowledge of RGA and SVD analysis. It will also require a student to use extensive knowledge of higher-order systems to model certain responses. All of these needs should create a challenging and engaging system for the students to undertake. Introduction The food industry has long been a frontier in cross-disciplinary work of both chemical and biological engineering. The food industry often faces the same issues of design from taking raw materials and cooking/reacting them into a highly-specified, large-scale product. Since the end product is assumedly a consumable food, sterile conditions and proper biological considerations are always a factor in process design. In scale up of large food production plants, there is a greater need for automation to meet such high throughput demands. However, strict constraints on quality control often require constant on-line and off-line testing and measurement. The screw-based food extruder has been an industrial standard in food processing for several decades due to its ability to mix, cook, compress, transport, and react ingredients simultaneously. The process is generally a single-unit operation that works similarly to a high-speed bioreactor. Feed ingredients are fed down at one end of the machine, where they are mixed by a (singleor twin-) screw that passes the ingredients down the length of the extruder. The extruder can then be carefully regulated for cooking by manipulating the extruder barrel temperature surrounding the mixing ingredients. The speed and temperature of the mixing chamber determines the amount of cooking, moisture, extent of mixing, and exiting temperature of the final product. Upon its exit, an extruder often will have a nozzle to compact, and a die to shape, the exiting product for cutting and further downstream processing and packaging. Currently, single-screw operations are the most common in plant use. However, the twin-screw extruder is the most newly-implemented and most studied because of its greater ability to manipulate individual operating parameters. A typical food extruder setup is shown in figure 1. Figure 1 – A cross-sectional diagram of a typical screw cooking food extruder with die cutter. Control History There have been a number of studies performed on the automated control of the twin-screw food extruders. There are three major groups recently working on the various aspects of this control problem that dominate the literature that will be discussed. All use slightly different control techniques and goals, but all use models based on experimental control of producing a cornmeal-based puffed snack. The common theme is to use the experimental data from pilot-scale units to develop transfer functions for controller design. Dr. Rosana Moreira at Texas A&M (Schonauer 1995, 1996, & 1997) has done a number of studies on extrusion using a color monitoring system over the final product to make assessments of moisture and cooking quality measurement correlations, as well as use of thermocouples and moisture gauges to determine thermal and die dynamics. The ultimate goal was to fully predict both on-line and off-line quality standards which can include: “color of extrudate, bulk density, expansion (diameter, lineal, ratio), texture (breaking strength), water solubility index (WSI), water absorption index (WAI), gelatinization, dextrinization, sensory attributes, dimensional (diameter and length), and surface texture”. The ultimate control systems involved manipulation of screw speed, feed rate, water rate, and barrel moisture. The models were developed to control motor torque, moisture content, product temperature, and specific mechanical energy. These experiments were then used to model processes for both GPC and MPC control. Another group out of the University of Newcastle in Australia (Wang 2001, 2004) designed several systems of MPC controllers using screw speed, motor torque, specific mechanical energy, and liquid injection rates as the manipulated variables. They found that die pressure and internal zone temperatures to not have enough direct control on many of the desired output product qualities to make proper manipulated inputs, a finding common to almost all the studies done in this area. Part of the process this group followed in order to develop minimally complex control strategies was a series of transfer function matrices to relate the most relevant inputs and output. However, many of these models were highly complex and involved dynamics way too complicated for our desired modeling basis. The final investigator of the twin-screw control problem is a Dr. Steven Mulvaney, a food sciences professor at Cornell University (Lu 1993, Singh 1994, and Haley 2000). Almost all the same manipulated inputs and output objectives of many of the other groups were used in the experiments, but with much more focus on developing a wide range of models. Over a series of several experiments, models over a wide range of operating conditions and model order were derived from the collected data. One paper in particular (Singh 1994) focused on low-order models for the use of MIMO PID control, which provided the data and basis for this control case-study. Extruder Setup The extruder examined in this case-study is a twin-screw extruder with manipulated inputs screw speed (SS) and moisture content (MC). The measured outputs of the system are the product temperature (PT) and the motor torque (MT). The disturbance input on the system is the fluctuation in the jacketed barrel temperature. All temperatures in the system are measured in Celsius, the screw speed is measured in revolutions per minute (rpm), and the motor torque and moisture content is a unitless percentage. The steady-state values, and the constraints on input range, are shown below: Table 1 – Values and ranges for inputs and outputs of plant model. Measured Value Steady-State Value Range of Manipulation Screw Speed 250 rpm 150-350 rpm (±100) Moisture Content 18% 13%-23% (±5) Barrel Temperature 121°C 101°C-141°C (±20)