Nonlinear Control Systems: Some Practical Methods

Stability Analysis of a Nonlinear Coupled-Core Reactor Control System

“…Equating Eqs. (11) and (12), one has [4,5].But unfortunately for nonlinear multivariable systems, there are infinite number of solutions which can satisfy this condition [13]. This is quite different from that of the single-input, single-output systems.…”

“…Fig.3 shows the wei and woj loci for N1 (a1) is fixed at 0.0163(i.e., Ai=1.703) while N2 (a2) is varying. From Fig.3(a), one can see that if the value of N (a2 ) is less than 0.0163 (i.e., A2 = 1.703), the roots wei and woj are alternative in sequence, then the corresponding system is stable [4,5,16].…”

“…In this paper, a general method based upon the stability-equation method [4,5] is proposed. The considered systems need not be symmetrical and reduced.…”

“…In addition, the systems may have both nonlinearities and adjustable parameters. The main approach of the proposed method is to analyze system stability and the existence of limit cycles by finding the simultaneous solutions of both the stability-equations [4,5] and the harmonic-balance equations [6][7][8][9][10][11][12][13]. T =Kn -aT1…”

Limit cycle prediction of a neurocontrol vehicle system based on gain-phase margin analysis

“…The traditional method of analyzing the amplitude and frequency of a limit cycle is to linearize the nonlinear elements according to the describing function method [1][2][3][4][5][6][7][8][9]. Recently, this method has been extended to analyze the stability of fuzzy [10,11] and neural systems [12,13].…”