This report is written to analyze the recitation that was presented on 02.04.2013. The recitation was presented by Sena TEMEL, Semih YAĞLI and Semih GÖREN. It was mainly about P, P-D, P-I and P-I-D controllers, their digital versus continuous time realizations and their characteristics including sampling period effects on the response of digital ones. Moreover, position and velocity form of P-I-D control was modeled on the ‘Gate’ project. Apart from these topics, P-I-D tuning methods such as manual tuning, Ziegler-Nichols tuning, Cohen-Coon tuning and MATLAB tuning method were discussed. Transient performances of P, P-D, P-I and P-I-D controllers were explained in detail. Modeling a discrete time P-I-D controller to control a continuous time plant was explained over a MATLAB code introducing the effect of sampling time and the choice of s*-domain to z-domain transformation method on MATLAB. It was explained how to remove poles that cause instability in discrete time by adding a new pole. Finally, it was shown how one could control the speed and position of the vehicle using discrete time P-I-D controller on the ‘Gate’ project.
Aim of the Recitation:
Aim of the recitation was to introduce the concept of Discrete Time P-I-D controllers and how they can be implemented on real life projects.
It was first intended to explain the usage of continuous time P-I-D controllers. In the first part of the recitation, it was aimed to show the how P, P-I, P-I-D controllers change the steady state response of the closed loop systems. Moreover, the methods to tune P-I-D controllers were introduced. It was meant to show that how hard it could get to properly tune a P-I-D controller. Secondly, it was intended to show how P, P-D, P-I, and P-I-D controllers affect the transient response of the closed loop system. It was meant to show how one can gain a feature but lose the other. Thirdly, it was intended to show how one should estimate the dynamics of the continuous time plant and use proper sampling time for discrete time P-I-D controller. It was also meant to show how changing transformation method may cause different pole locations on the z-plane. Lastly, it was intended to show how one could control the velocity and the position of the vehicle of the ‘Gate’ project by implementing a discrete time P-I-D controller in that project. 3
P controller is mostly used in first order processes with single energy storage to stabilize the unstable process. The main usage of the P controller is to decrease the steady state error of the system. As the proportional gain factor K increases, the steady state error of the system decreases. However, despite the reduction, P control can never manage to eliminate the steady state error of the system. As we increase the proportional gain, it provides smaller amplitude and phase margin, faster dynamics satisfying wider frequency band and larger sensitivity to the noise. We can use this controller only w...