PID-based controls in computing systems: a brief survey and some research directions <s> Networks with multiple clocks <s> Most wireless sensor networks (WSNs) employ a sleep clock to enable sensor on-off mode to save energy. Since the sleep clock usually works at a relatively low frequency, it is important to correct the long-term synchronization error caused by instability and nonlinearity. In this paper, the time synchronization issue in a WSN is formulated as a closed-loop control problem. Using the proportional-integral (PI) control principle, we propose a feedback-based synchronization (FBS) scheme to compensate the clock drift caused by both internal perturbation and external disturbance. Synchronization accuracy and FBS dynamics are analyzed in terms of response time and overshoot. We also derive a formula to determine the controller parameters for different synchronization accuracy and response-time requirements. Extensive experiments have been conducted to evaluate this synchronization scheme. The results indicate that FBS is much more robust than the delay measurement time-synchronization (DMTS) protocol in different synchronization durations and sensor node configurations. It is shown that FBS achieves almost the same accuracy as the flooding time-synchronization protocol (FTSP) when synchronization period P is less than 60 s, and it outperforms FTSP when P is longer than 60 s. Furthermore, the experimental results reveal that FBS's response to an external disturbance is faster than that of FTSP in one- or two-hop WSN scenarios. In addition, FBS consumes fewer resources than FTSP. <s> BIB001 </s> PID-based controls in computing systems: a brief survey and some research directions <s> Networks with multiple clocks <s> Control engineering approaches have been identified as a promising tool to integrate self-adaptive capabilities into software systems. Introduction of the feedback loop and controller into the management system potentially enables the software systems to achieve the runtime performance objectives and maintain the integrity of the system when they are operating in unpredictable and dynamic environments. There is a large body of literature that has proposed control engineering solutions for different application domains, handling different performance variables and control objectives. However, the relevant literature is scattered over different conference proceedings, journals and research communities. Consequently, conducting a survey to analyze and classify the existing literature is a useful, yet a challenging task. This paper presents the results of a systematic survey that includes classification and analysis of 161 papers in the existing literature. In order to capture the characteristics of the control solutions proposed in these papers we introduce a taxonomy as a basis for classification of all articles. Finally, survey results are presented, including quantitative, cross and trend analysis. <s> BIB002 </s> PID-based controls in computing systems: a brief survey and some research directions <s> Networks with multiple clocks <s> Time synchronization is crucial for wireless sensor networks (WSNs), where operations often rely on time ordering of events. WSNs are deployed in different scenarios, and therefore their timing requirements are often related to the peculiar characteristics of the specific environment they have to act in. Synchronization is anyway always an issue: transactional applications need monotonicity of the nodes’ clocks to avoid time reversal, ultralow power applications call for minimal overhead to allow for low-duty-cycle operation, applications facing extreme environments have to maintain the needed precision in the presence of unforeseen thermal drift, and so on. Specially, control applications on battery-powered devices, where timing is an issue and low-power operation is highly desired, benefit from synchronization. However, to date, the problem of synchronization has been differently faced depending on the application domain. This paper proposes a general solution to the problem of synchronization in WSNs, which seamlessly integrates with the radio stack. In addition, it guarantees monotonic and continuous node clocks with low overhead for the infrastructure. The solution is based on a decentralized control scheme that is stable and robust to thermal stress, without the need for temperature measurements. The control scheme is simulated and implemented on real WSN nodes. The efficiency of the scheme is evaluated with simulations and experiments, providing insights on the maximum synchronization error between nodes, on the communication overhead, and on the limited nodes’ power consumption. The solution is also compared with state-of-the-art alternatives. <s> BIB003
When synchronising a slave clock to a master that transmits a "sync" packet with fixed period T , the additive disturbance d is the accumulated slave clock skew over T , while the control signal u is naturally chosen to be an additive correction to the slave time, attempting to match T + u in that time to T in the master one (see BIB003 for a complete discussion). Hence, denoting by e the error, in this case (1) reduces to i.e., in transfer function form, In this case, the main source of disturbance is the temperature of the slave, that typically follows exponential transients with durations such that, over some synchronisation period, d significantly resembles a ramp. A PI is therefore not enough. To effectively reject the expected disturbance, it is convenient to prescribe the disturbanceto-output transfer function to have two unity zeroes, thus obtaining the controller C(z) from where α is a design parameter to trade error convergence speed versus high-frequency control sensitivity. This yields that can be interpreted as an ideal PID plus an additional integrator, or the cascade of two PIs. In this case the system is time-invariant, however, so that ensuring stability is a no-problem. The so obtained controller significantly outperforms state of the art alternatives like the Flooding Time Synchronisation Protocol BIB002 or the Feedback Based Synchronisation scheme BIB001 , as shown in the experiment of Figure 3 , where three wireless nodes carrying the three techniques (the proposed one is named FLOPSYNC-2 for Feedback-based LOw-Power SYNChronisation version 2) were subjected to a shade-sunlight transition causing a 20 • C temperature variation. Note the ramp-like aspect of the temperature disturbance over say 3-4 synchronisation periods: FTSP and FBS make the error settle when temperature settles, while FLOPSYNC-2, thanks to the disturbance-.tailored controller, acts in advance. For more details on the control synthesis in FLOPSYNC-2, the reader is referred to BIB003 .