Stability Analysis and Design of a Nonlinear Controller for Hot Rolling Coiler

Hindawi Publishing Corporation Discrete Dynamics in Nature and Society Volume 2015, Article ID 938287, 15 pages http://dx.doi.org/10.1155/2015/938287 Research Article Stability Analysis and Design of a Nonlinear Controller for Hot Rolling Coiler Rui Li,1 Chao-nan Tong,1 and Xu Yang1,2 1 School of Automation & Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, China 2 Correspondence should be addressed to Xu Yang; Received 29 August 2014; Revised 21 September 2014; Accepted 21 September 2014 Academic Editor: Qingang Xiong Copyright © 2015 Rui Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For the new style hot rolling coiler which adopt AC asynchronous motor as the driving force and with using the algorithm based on differential geometry design nonlinear controller, precise coiling tension control in the rolling process of strip steel is achieved. In this paper, under the rotating orthogonal coordinate system, the fifth-order nonlinear motor model is selected as the controlled plant. By multi-input multioutput (MIMO) exact feedback linearization (EFL) algorithm, the nonlinear model is transformed to a linear one. In terms of small-gain theorem, it is the first to prove that the nonlinear coiler engine that contains the controller has characteristics of input-to-state stability. Experimental results show that the algorithm can be used for high order tracking control system with time-varying parameters. Even without the traditional flux orientation calculation, the output signals are decoupled. With this controller, the tension deviation is restricted to less than 3% and average rotational speed bias was decreased from 0.5% to 0.1% that ensure high-quality plate cut and surface of strip products. 1. Introduction Constant tension is critical to uniform product thickness and smooth surface in rolling coiler. In the process of coiling, too big deviation of tension can directly lead to wrong layer, tower, loose volume, bowl volume and so forth. Through the adoption of effective control method, to improve quality of production is always the key point also the difficulty of coiling process. Because, in the process of the coiling strip, coil’s diameter changed randomly, this will cause the winding speed of the coiler to change unexpectedly. In order to make the rotor speed to coincide with winding speed and the rolling tension of steel strip to keep constant, the speed of the coiler should be adjustable at any time, and speed range should be changed to adapt to the changes in coil diameter. In nearly decade, due to the improvement of hydraulic drive system and the application of advanced power electronics inverter technology, more and more AC (alternating current) motor was used as the main power of equipment coiler. High maintenance cost and complex vector control system for AC synchronous motor were compared to the complex structure. Asynchronous motor structure is relatively simple and easy to be maintained and developed. So in many giant steel mills, more asynchronous motor is implemented in technological upgrading projects in recent years [1]. Consideration of the control mode with a constant ratio of voltage frequency in general inverter and traditional regulation system in AC asynchronous motor is difficult to realize the coiler constant tension control. In actual system, high-speed PLC programming algorithm with the nonlinear proportional integral differential (PID) control is often adopted [2]. AC asynchronous motor contains strong coupling and high-nonlinearity factors. For the purpose of implementing a wide range precise control of the motor in the electromechanical energy conversion process, common technologies are the vector control and direct torque control. However, nonlinear control theories have not been unified. Specifically for the plants that are expressed as high order affine or nonaffine nonlinear differential equation set, the stability analysis of solving algorithm is still a hot and difficult topic which has been widely concerned. Current mainstream subjects 2 about the advanced nonlinear control theorem include the passive theory, the inverse system method, the backstep approach, feedback linearization method, and active disturbance rejection control technology [3]. In the study of exact feedback linearization (EFL) for AC motor drive system, the applications in permanent magnet synchronous motor are relatively mature [4–7]. For asynchronous motor feedback exact linearization, especially for high order linearization problem of affine nonlinear systems, less detail theoretical derivation is found in the literature, for instance, the research on static two-phase coordinates of five orders linear affine nonlinear system [8, 9]. Under the rotating coordinate system, the reduced order induction motor model with accurate linearization control is discussed [10, 11]. But the problem of the stability analysis of an interconnected system that inferred from the theory of EFL controller has not been considered and solved yet. This paper just chooses the classical five-order induction motor system under rotating orthogonal coordinates as the controlled plant. High order tracking controller design method of affine nonlinear system is specified. Combined with small gain theory, the problem of the stability of an interconnected high order system that inferred from the theory of EFL controller is proposed. It is proved that the nonlinear control law for Brunovsky normalized form which refers to the EFL algorithm can stabilize the overall system. This application has not been considered yet in previous literatures. Before 90s in 20th century, besides the Lyapunov method, the input to state stability (ISS) approach was a feasible tool to analyze and design the stability of complex control systems. And input to output practical stability (IOpS) as a concept was introduced by Sontag in 1989 [12]. Michel and Miller initially analyzed time-varying nonlinear interconnected system. And the small gain theory as the mathematical basis of the ISS method is defined much earlier in 1977 [13]. By the end of the 20th century, validity of small-gain approach in the ISS framework on the occasion of two interconnected subsystems was proven in Jiang et al.’s research, which stated that the general interconnection of two IOpS systems is still an IOpS system [14]. It was demonstrated that global asymptotic stability can be ensured by a nonlinear combination of partial-state feedback [15]. Based on the small gain theory and the thought of quantized nonlinear computation, it is proposed that an interconnected system is decomposed into two parts and then, respective (...truncated)