Control design for the compensation of limit cycles in Van Der Pol oscillator

In nonlinear systems, unwanted oscillations and limit cycles may occur as a result of various effects such as peripheral strife, environmental interactions, physical parameters effect, variations of set-points. Such type of effects can be found in mechanical systems, electrical networks, and power systems. Van Der Pol oscillator is used as a prototype to describe and study the behaviour of nonlinear systems exhibiting limit cycles. These limit cycles produce undesired effects resulting in a wastage of energy in electrical circuits and physical damage in mechanical systems. This paper presents the implementation of a state feedback controller in the form of pole placement method and Proportional, Integrator and Derivative (PID) to eradicate the limit cycles produced in the event of Van Der Pol oscillator. A case study is also presented regarding the minimization of control efforts in order to improve the transient response and to cater the parameters uncertainties.