Design of Nonaffi ne Nonlinear Control Systems Based on Quasilinear Models

A new method has been developed for control systems design of nonaffine in control plants with differentiable nonlinearities and a measurable state vector. It is assumed that the equations of a nonaffine nonlinear plant are given in the Cauchy form. To solve the design problem, these equations, by including an integrator into the system, are converted to equations of an extended virtual affine in control plant. For this purpose, a quasilinear model of a nonaffine in control object is first created. This model describes the nonlinear plant with the same accuracy as the Cauchy equations. Then the quasilinear model of the extended virtual plant, which is affine in control, is formed on basis of the quasilinear model of the initial nonaffine plant, taking into account the added integrator. It is shown that if the quasilinear model of the initial object is controlled on the state, then the extended plant quasilinear model has the same property. This makes it possible to apply an algebraic polynomialmatrix method of nonlinear control systems design for the resulting extended model. The resulting closed nonlinear system is Hurwitz systems, its equilibrium is asymptotically stable, and it can be provided with the required duration of the transition under certain conditions. The controllability criterion output of the nonaffine nonlinear plant is established. This criterion differs from the similar criterion of the affine nonlinear plants only in that it takes into account the nonaffinity. This criterion is determined solely by the properties of the quasilinear model of the initial nonaffine plant. If the condition of this criterion is met, it is possible to ensure a zero value of the static error of a closed system according to the setting impact. The design procedure of nonaffine nonlinear control systems by the proposed method is analytical and consists in determining of quasilinear models, several polynomials and solving SLAE with functional coefficients. The procedure for applying the proposed method and its effectiveness are shown by the example design control system of the autonomous underwater vehicle motion. This method can be used to create control systems for nonaffine nonlinear plants of various purposes.