Abstract
Frequently a physical plant of a control system has an optimum operating point such as the spark (or injection) time of an internal combustion engine that results in maximum torque. Extremum Seeking Control (ESC) is a method of adaptive control capable of locating and maintaining a plant at such an optimum operating point in real time. It is capable of doing so with minimal a priori knowledge of the plant and can also track slowly varying changes. Input perturbed ESC schemes that use periodic dither signals have the disadvantage of requiring a high bandwidth for sampling and correlating the plant output with the dither signal. If the feedback path were to be implemented over a packet switched communication network, the high bandwidth requirement could result in increased congestion and consequently packet delays and dropouts. As a solution encoding using sporadic (aperiodic) sampling techniques can be used in the feedback path of the ESC scheme to reduce the required bandwidth. However, in order to ensure convergence of the ESC scheme with encoding, the effect of the signal reconstruction error due to encoding on the critical correlation stage has to be investigated. The contribution of this paper is an investigation of the convergence requirements and bandwidth performance of two encoding schemes; Memory Based Event Triggering (MBET) and Event Triggered Adaptive Differential Modulation (ETADM). The results show that MBET can fail for objective functions with plateaus. ETADM fails when the number of ETADM steps used for reconstructing the plant output per perturbation cycle are too low to allow correlation. In terms of bandwidth reduction MBET performs better than ETADM (97\% and 70\% respectively). However, the use of MBET results in a longer convergence time.
Highlights
When a plant is time invariant, known a priori and not subject to exogenous disturbances, finding an optimum operating point offline can be computationally intensive but achievable
In a networked control system (NCS) that is packet switched, when a periodically sampled variable is transmitted over the communication network it can be subject to the congestion related issues such as delay, delay variation, and packet drops as reported in Zampieri (2008), Donkers et al (2011), and Premaratne (2014)
The event-based sample is transmitted across the communication network and at the receiver a Zero Order Hold (ZOH) is used to reconstruct the original signal
Summary
When a plant is time invariant, known a priori and not subject to exogenous disturbances, finding an optimum operating point offline can be computationally intensive but achievable. Extremum Seeking Control (ESC) is a potential solution to this problem It is a type of adaptive control capable of seeking an optimal operating point and maintaining the plant near it. Beaudoin et al (2006) use ESC for bluff body drag reduction, while in Dixon and Frew (2006), it is used for optimizing sensor networks This technique is used for vehicle control in Stankovich and Stipanovic (2009). The main motivation for investigation is the effect of the reconstruction error of the above sporadic sampling techniques on the vital correlation stage of the ESC scheme
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