Operator-Based Robust Nonlinear Control for a Peltier Actuated Process

Recently, Peltier device has attracted much attention in cooling process industry. Peltier device is a kind of device with thermoelectric effect which contains three effects such as Peltier effect, Seebeck effect and Thomson effect1, 2. It can be used to cool or heat by Peltier effect and generate electric power by Seebeck effect. Thomson effect relates the rate of generation of reversible heat inside a homogeneous conductor with a temperature gradient23. Due to the Peltier effect, one side of Peltier device is endothermic and another side is radiation when an electric current is applied to it, and the hot side and cold side reverse when opposite current is applied22, 23. Because heating can be achieved more easily and economically by many other methods, Peltier devices are mostly used for cooling. Peltier cooler uses the Peltier effect to create a temperature difference between the two sides of the device. So, it is an interesting consequence that the Peltier effect is used to make a cooler. Due to compact size, not generating vibration noises and freon gas, the Peltier devices are widely used in many applications3, 4, 23. For example in the past years refrigerators used fluorocarbon generally. However, such refrigerators are prohibited gradually because it leads the disruption of ozone layers and affects the climatic change. So the Peltier effect is considered to create the refrigerator. Peltier devices are also commonly used in camping and portable coolers and for cooling electronic components and small instruments22. Peltier coolers can be used to cool computer components to keep temperatures within design limits without the noise of a fan, or to maintain stable functioning when overclocking23. Moreover, there are still some application products including some small wine coolers, some icing devices for medical treatment and so on. In this paper, we focus on the control aspects of a Peltier-based aluminum plate thermal process. Linear PID controllers or switching PID controllers are commonly used in Peltier-based thermal process due to their simplicity in both design and implementation24, 25. However, Peltier cooling performance is a function of ambient temperature, hot and cold side heat exchanger (heat sink) performance, thermal load, Peltier module geometry and Peltier electrical parameters24. Therefore, in general, the Peltier actuated process is a nonlinear control affine system. The output temperature depends not only on the current, but also on square of the current. For the complex nonlinear, it is difficult to achieve high control accuracy (±0.2°C) by using the mentioned PID controller designs, which is required in some applications such as laser frequency elements. Conventional nonlinear controller design techniques cannot also be applied since the dynamics model does not belong to the typical nonlinear control affine form3, 25. To resolve this problem, a robust nonlinear control technology is presented for an aluminum plate thermal process with the Peltier device by using operator-based robust right coprime factorization approach in this paper. Operator theory is an advanced control theory based on an idea that a signal in the input space is mapped to the output space and some researches in regards to the theory have been conducted5, 6, 11, 12. The relationship between the robustness of the right coprime factorization and the robust stability of the perturbed nonlinear system is shown by Chen and Han7, 14. Based on the design scheme a robust tracking control system is proposed by Deng et al. 10, 13, 18 and the perturbed signal does not affect the system output. So, the operatorbased control method can be applied to a broader class of nonlinear systems with perturbations. Furthermore, a method to control unstable systems with input constraints is given in ref 15, 17, 19 where the controlled system with the input constraints satisfies robust right coprime factorization. The advantage of the operatorbased control is that the control design is relatively simple because bounded input and bounded output stability is guaranteed21, 26. Based on the operator theory, nonlinear controller for the aluminum plate thermal process with Peltier device is designed by using robust right coprime factorization concept. That is, to ensure the robust stability, robust controller is considered and operator-based tracking filter is also designed to obtain the desired output tracking performance. As a result the designed control system is to ensure the robust stability and pursue the perfect output tracking performance. The effectiveness of the designed system is shown by the simulation and experiment. The contents of this paper are written as follows. Firstly, system architecture and function for Peltier actuated process is given. Then modelling of the thermal process is shown. Next, an operator-based robust stabilization controller is designed by robust right coprime factorization method. Meanwhile an operator-based tracking control is considered to satisfy tracking performance. Further, simulation and experimental results are given to confirm the proposed method. Finally we draw the conclusion on our current and show future work.