Simple and efficient PID algorithm design method for controlling first order systems with a time delay

Abstract

Many processes in industry are characterized by delay time or by slow aperiodic dynamics called lag behavior. In addition, many plants in the industry are described mathematically by higher order systems that are approximated with the lower order systems, most frequently such processes and systems are described mathematically as first-order-systems-with time-delay (FOSTD), also called first-order-plus-dead-time (FOPDT). The presence of time delays causes degradation and limitation of achieving desired performance, moreover, it can induce instability. In such cases, design of feedback control algorithm becomes difficult and tedious task. The present work suggests an efficient, simple, linear, and easy to apply design expressions for designing continuous PID (proportional-integral-derivative) control algorithm modes to control the behavior of FOPDT systems. The design expressions are intended to overcome negative effects of time delay presence, as well as, to simplify the control algorithm design process and help designer, in easy and simple way, to get system under control with acceptable system stability, medium fastness of response and without or with minimum possible overshoot, oscillation and error. For testing and evaluating the correctness, applicability and efficiency of the derived expressions, MATLAB/Simulink software was applied to develop refined software simulation model that simulates real life values and returns maximum needed numerical and graphical data for assessment process. In addition, various FOSTD systems’ types and forms were used in the simulation model, in particular, systems with small, medium and large time constants, DC gains, and time delay, unstable systems, systems with variable delay. Furthermore, to assess the efficiency of suggested design expressions, the resulted overall system response were compared with resulted responses when two design methods were applied; worldwide known Ziegler Nichols method and MATLAB/Simulink auto-tuned PID block. Analysis of numerical and graphical testing results, show that, The designed control algorithm applying the suggested expressions can, not only simplify the design process, but also, efficient for successful in getting system under control and improving controlling system performance, speeding up response, reduce overshoot, and minimize error, but also stabilize an unstable plants.