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In this paper, we propose a modeling and design technique for a proportional-integral-derivative (PID) controller in the presence of aperiodic intermittent sensor measurements. Using classical control design methods, PID controllers can be designed when measurements are available periodically, at discrete time instances, or continuously. Unfortunately, such design do not apply when measurements are available intermittently. Using the hybrid inclusions framework, we model the continuous-time plant to control, the mechanism triggering intermittent measurements, and a hybrid PID control law defining a hybrid closed-loop system. We provide sufficient conditions for uniform global asymptotic stability using Lyapunov set stability methods. These sufficient conditions are used for the design of the gains of the hybrid PID controller. Also, we propose relaxed sufficient conditions to provide a computationally tractable design method leveraging a polytopic embedding approach. The results are illustrated via numerical examples.
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Proportional Integral Derivative Control in Spark Plasma Sintering Simulations
The prediction of microstructure evolution and densification behavior during the spark plasma sintering (SPS) process largely depends on accurate temperature regulation. A loop feedback control algorithm called proportional integral derivative (PID) control is a practical simulation tool, but its coefficients are often determined by an inefficient “trial and error” method. This paper is devoted to proposing a numerical method based on the principles of variable coefficients to construct an optimal linear PID controller in SPS electro-thermal simulations. Different types of temperature profiles were applied to evaluate the feasibility of the proposed method. Simulation results showed that, for temperature profiles conventionally used in SPS cycles, the PID output keeps pace with the desired profile. Characterized by an imperfect time delay and overshoot/undershoot, the constructed PID controller needs further advancement to provide a more satisfactory temperature regulation for non-continuous temperature profiles. The first step towards a numerical rule for the optimal PID controller design was undertaken in this work. It is expected to provide a valuable reference for the advanced electro-thermal modeling of SPS.
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- Award ID(s):
- 1900876
- PAR ID:
- 10222136
- Date Published:
- Journal Name:
- Materials
- Volume:
- 14
- Issue:
- 7
- ISSN:
- 1996-1944
- Page Range / eLocation ID:
- 1779
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/ma14071779
