Modeling and control of under-damped second order systems with dead-time and inverse response

Systems with inverse response are difficult to be identified because of the existence of at least one zero at the right half s-plane. However, it is important to obtain the transfer function as accurately as possible for such systems to be able to provide the desired performance using a controller. If the system has dead-time, the design problem becomes more complicated. This paper presents a new modeling method for under-damped second order systems with an inverse response to overcome the difficulties both in the analysis and design. Besides, a PID controller design in discrete-time domain is also introduced to provide a good performance in the closed-loop. The performance of the proposed modeling and control technique is demonstrated on an example using simulations.