The error is a result of both disturbances and unmodeled system dynamics

The World Health Organization and International Labor Organization have confirmed that long working hours of 55 or more weekly hours are an occupational risk factor for cardiovascular disease. Our study’s findings on sleep hours and related issues align with a pre-pandemic Washington state prison study, in which the majority of correctional staff and healthcare workers had less than five hours of sleep, 53% had zero to two hours of sleep between work shifts, and 40.7% to 47.2% of participants reported over thrice-weekly trouble falling asleep and nightly waking. In contrast, among East U.S. correctional healthcare workers during the pandemic, 81.57% did not have sleep disturbances, indicated by normal score ranges, but their mean sleep disturbance scores were significantly higher compared to correctional officer mean scores. The prison nurse study participants experienced higher pandemic-related work demand, schedule, and environment adjustments through increased COVID-19 patient care, increased night shift assignments, and increased department redeployment requests. The elevated California correctional facility COVID-19 case rate may have contributed to these occupational changes. Furthermore, a 2022 report from the National Commission on Correctional Health Care featured the ongoing issue of under staffing among certified correctional health professionals throughout the two years of the pandemic. COVID- 19 patient contact, shift assignment, and department redeployment work changes were similarly identified as challenges in the pandemic experience of U.S. hospital nurses. COVID-19 patient care has been associated with increased risk of infection, anxiety,nft vertical farming and emotional distress among nurses working in hospitals and other clinical settings.

The perception of adequate PPE supply may have been related to the lower degrees of COVID-19 general and work infection fears, despite significantly increased COVID-19 patient care among prison nurses. In contrast, among community nurses, there was a higher proportion that perceived inadequate PPE supply, elevated COVID-19-related fears, and a lower proportion of COVID-19 patient care. The perception of adequate PPE availability has been previously associated with a reduced probability of COVID-19 infection among U.S. healthcare workers across multiple clinical settings. The history of the CDCR’s mandatory overtime practice and our prison nurse study participants’ long working hours and COVID-19-related work changes exemplify the influence of occupational policy on nurses’ health and well being, as well as highlight implications for organizational interventions. A scoping review of nurses’ coping during COVID-19 emphasized the importance of work hour and schedule flexibility and occupational safety via PPE and training, encompassing organizational responsibilities. Considering our findings of elevated work hours and COVID-19 patient care, lowered sleep hours, and sleep quality issues, our sample of prison nurses may be at risk of high fatigue. There have been associations of increased work hours and COVID-19 patient care with increased fatigue among hospital nurses working through the pandemic. Although other nurse- and work-related stress instruments have been used within this population before the pandemic, the ERI instrument has not been previously applied to correctional nurses to measure occupational stress. The similar mean E–R ratio scores among the prison and community nurses corroborate previous ERI results from other nurse and healthcare worker populations working through the pandemic.

Italian hospital healthcare workers had a mean E–R ratio over 1, and three-fourths of nurses working in Greek hospitals scored E–R ratios over 1, demonstrating occupational stress in the context of the COVID-19 pandemic . In contrast, pre-pandemic studies among correctional officers in China and general nurses in Europe indicated a mean E–R ratio score under 1. With respect to the findings of our study, it is suggested that the current pandemic circumstances may contribute to increased occupational stress in all types of nurses. Addressing the high levels of occupational stress suggested by both nurse groups may imply feasible approaches with symptom reduction interventions. The published reviews of individual-based nurse intervention studies have identified evidence of mindfulness interventions as being helpful in the reduction of work stress and burnout, as well as the prominent use of technological mediums to promote intervention accessibility. Therefore, potential interventions to reduce stress among nurses working in prisons and within the community may involve mindfulness techniques administered through a digital format. Regarding psychological measures, the high prevalence of PTSD symptoms in our study contrasts with the findings of previous studies on correctional healthcare workers. Pre-pandemic Canadian studies that categorized nurses within a minority subgroup of correctional wellness workers found a lower prevalence of positive PTSD screens, at 16.7% and 17.2%, which suggests the pandemic’s effect on correctional healthcare worker post traumatic stress symptoms. Considering the COVID-19 pandemic, our study’s psychological findings differ from those of a recent East U.S. correctional worker study. Almost half of our prison nurse group had positive PTSD screens, while in the latter study, 43.27% of correctional healthcare workers had normal PTSD scores and 20.29% had moderate and severe scores.

Both our prison group and the East U.S. healthcare worker subgroup had a low prevalence of depression and anxiety screens. The prevalence contrasts among these studies may be due to differences in instrumentation, timing, and setting. Although the scope of our study may not provide causal inferences, our prison group’s higher prevalence of PTSD may be related to our single-site focus and a previous finding among hospital nurses of significantly elevated PTSD scores associated with COVID-19 patient care. This study had the following limitations, including its relatively small sample size. Our findings from one California prison may not be generalizable to all California prisons, nor the whole correctional nurse population. Although most of the nurses in the community group were from California and worked in hospital settings, the heterogeneity of this group may present a nonequivalent comparison to the single-site prison nurse group due to potential differences in the work settings. The extended and nonover lapping survey windows of the two groups also present the possibility of different historical effects affecting each group. The self-report nature of the survey and the retrospective items referring to before the pandemic may have introduced recall bias. Regarding the possible generalizability between our study participants and the correctional and general U.S. nurse populations, the demographics of our study participants reflect those of the 2020 U.S. nurse population estimates, with a female and White majority. However, the sample and population estimate distributions under represent male nurses and nurses of other ethnicities, warranting future research to investigate the occupational experiences and needs of these minority groups. The study’s strengths include its timing within the first year of the COVID-19 pandemic,indoor vertical farming which provides data of the pandemic’s initial impact on the prison and community healthcare settings. Despite limitations from the study design decision to retroactively add the prison nurse group, this addition contributes to the representation of the correctional nurse population. Likewise, the allowance of one- to two-month survey windows and the use of short-form versions of validated instruments were intended to accommodate participants’ time and stress while working during this phase of the COVID-19 pandemic. The comparative study design between a specialized nurse group and a general nurse group, rather than a different occupation, highlights the needs and circumstances of prison nurses. The participants in both study groups were experienced nurses, with a minimum of 2 years and a mean of about 15 years of work, which avoids potential confounding from newer nurses transitioning into the practice. This study addresses the geographical and nursing specialty knowledge gaps by providing data on Californian prison nurses. Although the prison nurse group sample size was small, our study may be considered a pilot study, contributing knowledge related to the COVID-19 pandemic in the context of the need for data on the correctional nursing workforce. The control of a jet injected into quiescent surroundings or into a cross flow is a fundamental problem with application to a wide range of engineering systems, particularly those for propulsion and energy generation.

In turbine engines, for example, active control of the jet in cross flow has been shown to improve the spread and penetration of the jet into the cross flow for dilution jet injection and improve boundary layer attachment at low turbine inlet Reynolds numbers for turbine blade cooling. Control of the jet in cross flow is typically accomplished through temporal excitation of the jet fluid using flow rate modulation or acoustic forcing. The excitation is periodic, usually with the goal of forming either sinusoidal or pulse-like jet velocity profiles. In practice, feedback control is required to shape the jet velocity since open-loop methods show significant amount of ringing and asymmetry compared to the reference wave forms .The field of repetitive control, which addresses asymptotic disturbance rejection and reference tracking of periodic signals, provides a framework for pulsed jet reference tracking. Systems based on repetitive control commonly use a time delay in the feedback loop to place an infinite number of poles on the imaginary axis at This work is sponsored by the National Science Foundation under grant no. CBET-0755104 C. Hendrickson and R.T. M’Closkey are with the Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA, 90095 USA rtm@seas.ucla.edu the fundamental frequency and harmonics of the periodic disturbance or reference. In practice, the plant has a finite bandwidth, therefore, only a finite number of internal models are required for asymptotic tracking. In this case, modulated-demodulated control can be used as an alternative to time delay repetitive control. Modulated-demodulated control, also referred to as adaptive feed forward control or adaptive feed forward cancellation, demodulates the spectrum of “high” frequency oscillations to base band signals, operates at base band, and then modulates the base band spectrum back to high frequency. In the pulsed jet experiment, the plant represents the dynamic system from the actuator command to the hot wire anemometer measurement at the jet exit. At high forcing amplitudes the jet velocity, if following a periodic reference, exhibits nontrivial coupling between harmonics that can destabilize the closed-loop system with a controller designed for more moderate forcing amplitudes. We show that identification of the plant dynamics in the base band coordinates provides key insight into the nonlinearity that couples adjacent frequency “channels” and provides a convenient means for compensating the coupling. In fact, the nonlinear coupling can be modeled in the base band coordinates as a MIMO constant gain. This control strategy achieves asymptotic tracking of the jet velocity within the bandwidth of control. A schematic of the experimental pulsed jet injection apparatus is shown in Fig. 1. Compressed air, regulated to maintain a constant mean jet velocity of 8ms−1 , flows into a plenum then through a smoothly contracted nozzle into quiescent surroundings. The jet velocity is perturbed about its 8ms−1 mean value by a lightweight piston positioned at the bottom of the plenum. The piston is driven inline with the jet by a modal shaker. The shaker voice coil current is proportional to the shaker amplifier input signal. The amplifier input signal is the plant input. The jet velocity is measured using a hot wire anemometer placed in the center of the jet at the nozzle exit. Additionally, the apparatus is equipped with a microphone located at the top of the plenum. The controllers are implemented in Matlab’s XPC Target application with a 25kHz sampling rate. Two, 8-pole low pass Chebyshev filters with 10kHz corner frequencies filter the microphone and hot wire signals prior to sampling. We demonstrate our control technique without cross flow, however, the entire system can be placed beneath a wind tunnel with the nozzle exit flush with the test section floor if a cross flow is desired. Linear models of the pulsed jet can be developed from data generated with low amplitude test inputs. Controllers developed using the models are then adequate for low amplitude reference tracking. At RMS amplitudes exceeding 0.5ms−1 RMS, though, the nonlinear response of the velocity measurement can destabilize the closed-loop system with these controllers. The desired velocity perturbation is periodic so the nonlinear response can be studied from the point of view of coupling among harmonics in the periodic waveform. The magnitude and character of the harmonic coupling is dependent upon the desired velocity reference and the mean jet velocity. In general, the velocity output at given harmonic is a function of the input energy at all harmonics. For example, the velocity “frequency response”, shown in Fig. 2, is measured using band-limited white noise inputs with amplitudes set to perturb the jet velocity by 0.15ms−1 RMS and 0.80ms−1 RMS .


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