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| E. П. Пoпов Harmonic Linearization and Simulation of DC Double Closed-Loop System |
| Li Yuanping1, 2, Zhou Youqing2 |
| 1. Hunan University Changsha 410082 China 2. Changsha University of Science and Technology Changsha 410114 China |
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Abstract Nonlinear elements of speed control systems always lead to self-oscillations. The method of E. П. Попов harmonic linearization has been well-known to provide frequency criterion for stability of such oscillations. It had the contribution of correcting the values of elements after parameters of certain oscillation had been set formerly for better performance. However, the un-sufficient attention was paid in use under practical conditions of this method in modern control systems because it was quite difficult to calculate the necessary and precise values of the method especially when high-dimensioned matrix was employed in discussion. In the present paper Matlab and Mathematica are introduced as new expressions to construct Е.П.Попов models and obtain simulation results in DC double closed-loop control system. Thyristors and speed controller are respectively researched as nonlinear elements leading to self-oscillation. The Fourier series-based models of two elements are constructed. The analysis of stability and correcting of self-oscillation are accomplished. The simulation shows that the proposed combination of advanced mathematical tools and Е. П. Попов methods can lead to a novice way of controlling self-oscillations.
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Received: 17 November 2009
Published: 07 March 2014
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2011, Vol. 26 
