Phase plane analysis i nathan p ueger 28 november 2011 1 introduction this lecture and the next focus on the analysis of systems of di erential equations of the form considered last time. Mct pdf notes part b units topics covered epu pdf notes of part b units are listed below. Transmembrane spike potentials from sartorius muscle fibers of. Saintpetersburg state university of aerospace instrumentation. Pdf nonlinear stability analysis of phase plane is one of the most classic and effective methods. Phase plane analysis phase plane analysis is a graphical method for studying secondorder systems. Studied here are planar autonomous systems of differential equations. Generalized isocline method of plotting phaseplane trajectories. The main setting in which we will study these systems is by analyzing the phase plane, which is a. Another approach, presented in this chapter, is geometrical in. Mct pdf notes unit 7 units topics covered epu pdf notes of unite unit 7 are listed below. Phase plane method is applied to autonomous second order system system response. Phase plane analysis for vehicle handling and stability. Linear systems there are many differential equations, especially nonlinear ones, that are not susceptible to analytical solution in any reasonably convenient manner.
Generalized isocline method of plotting phaseplane trajectories article pdf available in ieee transactions on automatic control 101. Mct pdf notes part b eee branch downloads smartworld. Pdf generalized isocline method of plotting phaseplane. Isoclines for first and secondorder linear differential equations are straight lines. There are a number of methods for constructing phase plane trajectories for linear or nonlinear system, such that socalled analytical method, the method of. Threaded orbits are added to show what happens to solutions that are plotted on longer and longer tintervals. This chapters objective is to gain familiarity of the nonlinear systems through the simple graphical method.
Phase plane trajectories of the muscle spike potential core. Numerical methods provide one means of dealing with these equations. Modern control theory notes mct part b unit 5 pole. Phase plane analysis concept of phase plane analysis. Mct pdf notes unit 7 eee branch downloads smartworld. The use of method of phase portrait presents changes in. Pdf in this article phase plane trajectories of stochastic processes are investigated. Modern control theory notes mct unit 7 phase plane method. The phase plane method is concerned with the graphical study.
Phase plane analysis is a nonlinear stability analysis method. Nonlinear control systems, analytical methods atherton. Phase plane analysis nonlinear stability analysis slideshare. Pdf phase plane analysis for vehicle handling and stability. A quick guide to sketching phase planes uc berkeley mcb. Other useful features and the results of phase plane recording are pre sented below.1008 1407 787 899 155 822 1601 802 54 82 203 90 159 343 1302 617 632 1011 1152 223 1375 1136 451 937 937 578 664 1260 260 1136 541 831 38 1453 565