Using Computer Algebra for Design of Nonlinear Control Systems

A rich collection of analytical tools based on differential geometric methods has been developed for the analysis and design of nonlinear control systems. The concept of feedback equivalence among nonlinear systems is used to linearize and control certain classes of nonlinear control systems. The left and right invertibility of nonlinear systems is used to solve the output tracking problem. Using computer algebra programming methods, a software system has been developed which makes these analytical procedures available to users who need not have an extensive knowledge of differential geometry. Examples of the use of this system are reported

Using Computer Algebra for Design of Nonlinear Control Systems.

A rich collection of analytical tools based on differential geometric methods has been developed for the analysis and design of nonlinear control systems. The concept of feedback equivalence among nonlinear systems is used to linearize and control certain classes of nonlinear control systems. The left and right invertibility of nonlinear systems is used to solve the output tracking problem. Using computer algebra programming methods, a software system has been developed which makes these analytical procedures available to users who need not have an extensive knowledge of differential geometry. Examples of the use of this system are reported

Qualitative Analysis of an Axial Compressor Model With Non-Constant Speed

In this research we have addressed the study of the qualitative behavior of nonlinear variable speed axial compressors model exhibiting surge and stall instabilities. Such a study can shed some light on the development of an effective control approach being capable of simultaneously controlling the speed and instabilities. The controller can stabilize the system around an effective operating point and improve performance and reliability of variable speed axial compressors widely used in aeronautic industries. Although previous studies [1, 2] have focused on developing a model for non-constant speed axial compressors, qualitative characteristic of such a model is still unclear and its active control including both rotating stall and compressor speed is still a challenging problem. In this study we are particularly interested in investigating effects of the acceleration of the compressor rotor on qualitative properties of the model. To this end, bifurcation analysis of an axial compressor model with spool dynamics was performed and the simulation of the model was developed along the way. Preliminary surprising results revealed that the type of instability, surge or rotating stall, not only depends on the final speed as thought before but is also deeply affected by the rate of the rotor acceleration. Impacts of the initial speed on the qualitative properties of the model were demonstrated as well. Furthermore previous work [1, 2] showed that amplitudes of stall harmonics grow during the speed transition and cause a temporary pressure drop at the compressor output. Our simulation results supporting the bifurcation analysis of the model revealed that during speed transitions both amplitudes of high order stall harmonics and the number of dominant harmonics also depend on the rate of the acceleration and the initial speed.</jats:p

Computer Algebra for Analysis and Design of Nonlinear Control Systems.

A rich collection of analytical tools based on differential geometric methods has been developed for the analysis and design of nonlinear control systems. The concept of feedback equivalence among nonlinear systems is used to linearize and control certain classes of nonlinear control systems. The left and right invertibility of nonlinear systems is used to solve the output tracking problem. Using computer algebra programming methods, a software system has been developed which makes these analytical procedures available to users who need not have an extensive knowledge of differential geometry. This work may be viewed as a component of an expert system for the treatment of stochastic and deterministic linear and nonlinear control problems. Examples of the use of this system are reported

Analytical Model of One Flexible Link System With Nonlinear Kinematics

The dynamical model of a flexible Euler–Bernoulli link system subject to high-speed motions is developed. Nonlinear kinematics are considered to take into account the foreshortening effect of the link. A continuous model with boundary conditions is derived using Hamilton's principle and spatially discretized dynamical equations are derived using Lagrange's equation based on the expression of the kinetic and potential energies of the flexible link system. The effect of the links foreshortening on the dynamical response is shown for a sinusoidal torque input at the links hub. The simulation results showed that for small torque amplitudes the difference between linear and nonlinear kinematics is small. However, for large amplitudes, this difference is prominent. </jats:p