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This analysis demonstrates PID+ control improves robustness in nonlinear systems with discrete-time models, highlighting industrial applications.
In modern industrial automation, control of nonlinear systems with complex dynamics poses significant challenges, especially when dealing with discrete time models that incorporate state-dependent parameters. Addressing this need, this paper explores the Proportional-integral-derivative-plus (PID+) control approach applied to nonlinear systems characterized by state-dependent parameter (SDP) discrete-time models. Two industrial applications are demonstrated as follows: a bitumen tank system and a reeling/packing machine used in a bitumen membrane sheet production line. Both systems are modeled using discrete-time transfer functions with SDP structures. The present work extends the novel SDP-PID+ approach by formulating its control algorithms and integrating additional proportional and input compensators. This enhancement enables effective and intuitive handling of processes characterized by discrete-time transfer functions with any order and sampling time delay. The approach enables a straightforward implementation of the SDP-PID+ algorithm across two distinct industrial applications, considering their varying response times. The approach reduces the time required to design the SDP-PID+ method for the selected applications while also demonstrating enhanced robustness and performance. It effectively mitigates disturbances and accommodates nonlinearities, higher-order dynamics, and delays.
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E. M. Shaban (2025) studied this question.
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