Competent and uncomplicated PID control algorithm design expressions for controlling second order systems

Proportional-integral-derivative (PID) control algorithm with its various forms, namely P (proportional), PI (proportional-integral), PD (proportional-derivative), PID, and compensators, is considered the most applied and widely used control algorithms in industry; this is because of its simple construction, robustness and capabilities to achieve desired control over plant performance. Designing PID algorithm is accomplished with a compromise to result in an overall system responds with acceptable levels of stability, response fastness, smoothness and costs. Various PID design methodologies and expressions have been introduced in text and literature,each has its advantages, disadvantages and limitations. In the present work, a new, efficient, simple, easy to apply and linear expressions for PID algorithmP-. PI, PD, and PID modes design are derived and presented. Expressions are derived based on relating parameters of both controller and plant. The expressions are intended to control the behavior of second order systems and approximated as such systems, such that it responds with acceptable stability level, minimum possible overshoot, oscillations and steady state error. To further improve the resulted response, only one tuning parameter α, is introduced To test, analyze, and evaluate the design expressions, MATLAB/Simulink software was used. A simulation model was built by integrating the next sub-models; PID control algorithm modes, drive with limitation and saturation blocks, sensor, desired output signal generator and finally various forms of second order systems. The simulation model was developed and refined to be as close as possible to real life conditions and processing. Studying the recorded testing, graphical and numerical results show that the suggested expressions are being simple and easy to apply, and also efficient in providing better control over controlled system’s behavior in terms of response measures and performance indices.Moreover, expressions are efficient to speed up response and eliminate or reduce overshoot, rise time and settling time. Studying results show that, the overall system responds with acceptable fast response, in most cases without overshoot, oscillation and with minimum steady state error and better ISE and IAE indices values.