This article presents an operator-based robust control method for nonlinear systems with Prandtl-Ishlinskii (PI) hysteresis On the existence of the hysteresis, the system usually exhibits undesirable oscillations and even instability While addressing the hysteresis, PI model is adopted to describe it Especially, the PI model is decomposed into two terms: an invertible part and a disturbance part In this way, the invertible part could be considered as a part of the nonlinear system Based on the concept of Lipschitz's operator and the robust right coprime factorisation condition, a robust control design scheme is given to guarantee the bounded input bounded output stability of the obtained system Further, a tracking operator design method is given to ensure the control system output-tracking performance under the existence of the disturbance part Numerical simulation results are presented to validate the effectiveness of the proposed method

Operator-based robust control for nonlinear systems with Prandtl-Ishlinskii hysteresis

In this article, operator-based robust nonlinear control system design for multi-input multi-output (MIMO) plants with unknown coupling effects is considered. That is, by using operator-based robust nonlinear control design, coupling effects existing in the MIMO nonlinear plants can be decoupled based on a feedback design and robust right coprime factorisation approach, the coupling effects caused by controllers and plant outputs can be stabilised by using definition of Lipschitz operator and contraction mapping theorem, and output tracking performance can be realised by a tracking design scheme. Finally, a simulation example about temperature control process of 3-input/3-output aluminum plate is given to support the theoretical analysis.

Operator-based robust nonlinear control system design for MIMO nonlinear plants with unknown coupling effects

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.

https://journals.sagepub.com/doi/pdf/10.1177/002029401104400404

Operator-Based Robust Nonlinear Control for a Peltier Actuated Process

In this article, operator-based robust control design for nonlinear plants with perturbation is considered by using robust right coprime factorisation approach. In detail, the property of unimodular operator is studied, and a control design structure is proposed. Based on the proposed design scheme, the designed system is robustly stable. Also, output tracking performance can be realised simultaneously. Finally, the effectiveness of the proposed design scheme is demonstrated by a simulation example.

Operator-based robust control design for nonlinear plants with perturbation

In this paper, a robust nonlinear control design using an operator-based robust right coprime factorization approach is considered for vibration control on an aircraft vertical tail with piezoelectric elements. First, a model of the aircraft vertical tail is derived to describe vibration response using the operator-based approach, where, to stabilize vibration of the tail, piezoelectric elements are used as actuators and a hysteresis nonlinear property of piezoelectric actuators is considered. Simultaneously, positions of the piezoelectric actuators that are stuck on the plate are arranged by using a finite element method. Then based on the obtained operator-based model, a robust nonlinear feedback control design is given by using robust right coprime factorization for the aircraft vertical tail with considering the effect of hysteresis nonlinearity from piezoelectric actuators. In particular, low-order modes are employed to design the control scheme even though vibration is configured by high-order modes...

Operator-based experimental studies on nonlinear vibration control for an aircraft vertical tail with considering low-order modes:

Most real plants must deal with some non-linear characteristics. For the non-linear plants, design of non-linear control system using operator-based robust right coprime factorisation is considered. The considered non-linear control system applications show the desired results. In this paper, operator-based non-linear vibration control of a flexible arm experimental system with uncertainties using robust right coprime factorisation is considered. In general, the vibrations by the characteristic vibration mode include from one to infinite order vibration modes and appear on the arm vibration. It is difficult to consider all vibration modes. Consequently, based on the concept of Lipschitz operators and robust right coprime factorisation condition, robust stability of the closed-loop system with unconsidered vibration modes as uncertainties is guaranteed, and desired vibration control performance actuated by piezoelectric element is ensured. Finally, simulation and experimental results are presented to support the effectiveness of the proposed design.

Yusuke Baba

Papers

Operator-based non-linear vibration control system design of a flexible arm with piezoelectric actuator