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Introduction to Feedback Control Systems
Published in Ramin S. Esfandiari, Bei Lu, Modeling and Analysis of Dynamic Systems, 2018
The final term in a PID controller represents the derivative control. The complete three-term controller is given by Equation 10.37. The main reason to introduce the derivative control is to increase the damping and thus to improve the stability of the system.
Optimal error governor for PID controllers
Published in International Journal of Systems Science, 2021
Luca Cavanini, Francesco Ferracuti, Andrea Monteriù
Proportional–Integral–Derivative (PID) controllers are used in a wide range of fields, e.g. process control and power converters, micro-manipulation and aerospace. PID algorithms are present in different forms in more than of the overall control loops developed (Åström & Hägglund, 2001), as standard single-loop controllers or as part of hierarchical, programmable or distributed control systems (Cavanini, Cimini, et al., 2017; Cavanini, Colombo, et al., 2017; Shi & Yang, 2018; Song et al., 2017). Despite the advanced control technology development of the last 20 years, PID still remains the most popular approach, due to the simple structure, conceptually easy to understand and provide adequate performance in the vast majority of applications (Liu & Daley, 2001). In fact, the three terms defining the PID control law fulfil the three most common required control performance: the proportional term provides a fast response to the actual error value without guaranteeing a good steady-state accuracy; the integral term, providing a slower response, yields the steady-state zero error and rejection of constant disturbances; the derivative term addresses fast error dynamics and is usually used in conjunction with filters to limit sensor noise effects (in this case, the controller is usually indicated as PIDF) (Knospe, 2006).