Signaling pathways consisting of phosphorylation/dephosphorylation cycles with no explicit feedback allow signals to propagate not only from upstream to downstream but also from downstream to upstream due to retroactivity at the interconnection between phosphorylation/dephosphorylation cycles. However, the extent to which a downstream perturbation can propagate upstream in a signaling cascade and the parameters that affect this propagation are presently unknown. Here, we determine the downstream-to-upstream steady-state gain at each stage of the signaling cascade as a function of the cascade parameters. This gain can be made smaller than 1 (attenuation) by sufficiently fast kinase rates compared to the phosphatase rates and/or by sufficiently large Michaelis-Menten constants and sufficiently low amounts of total stage protein. Numerical studies performed on sets of biologically relevant parameters indicated that ∼50% of these parameters could give rise to amplification of the downstream perturbation at some stage in a three-stage cascade. In an n-stage cascade, the percentage of parameters that lead to an overall attenuation from the last stage to the first stage monotonically increases with the cascade length n and reaches 100% for cascades of length at least 6.

Packetized energy management (PEM) is a demand dispatch scheme that can be used to provide ancillary services such as frequency regulation. In PEM, distributed energy resources (DERs) are granted uninterruptible access to the grid for a pre-specified time interval called the packet length. This results in a down ramp-limited response in PEM for DERs that can only consume power from the grid. In this work, a linearized virtual battery model of PEM is provided that is capable of predicting the down-ramp limited output of PEM and is used in a model predictive control (MPC) framework to improve the performance of PEM in tracking an automatic generation control (AGC) signal. By performing statistical analysis on the AGC regulation signal, PJM Reg-D, an ARMA model is derived as a predictor for the MPC-based precompensator. Finally, as an alternative to MPC, it is shown that by varying the packet length as a function of time, for example through packet randomization, frequency regulation can be improved under PEM.

In this paper, we consider the problem of constraint management in Linear Periodic (LP) systems using Reference Governors (RG). First, we present the periodic-invariant maximal output admissible sets for LP systems. We extend the earlier results in the literature to Lyapunov stable LP systems with output constraints, which arise in RG applications. We show that, while the invariant sets for these systems may not be finitely determined, a finitely-determined inner approximation can be obtained by constraint tightening. We further show that these sets are related via simple transformations, implying that it suffices to compute only one of them for real-time applications. This greatly reduces the memory burden of RG, at the expense of an increase in processing requirements. We present a thorough analysis of this trade-off. In the second part of this paper, we discuss two RG formulations and discuss their feasibility criteria and algorithms for their computation. Numerical simulations demonstrate the efficacy of the approach.

This paper considers the problem of controlling rotating machinery with actuators and sensors fixed in inertial space. Such a problem arises in control of charging and fusing stages in the xerographic process, drilling and milling machines, and turbo machinery. If a rotating device is represented as a set of discrete wedges, the resulting system can be conceptualized as a set of plants (wedges) with a single actuator and sensor. In such architecture, each plant can be controlled only intermittently, in a stroboscopic manner. This leads to the problem of cyclic control (CC) considered in this paper. Specifically, the problem of stabilizability in CC architecture is considered, and the resulting stabilizability conditions are compared with those in the usual, permanently acting control (PAC). In this regard, it is shown that the domain of asymptotic stability under CC is an open disc in the open left half plane (OLHP), rather than the OLHP itself, and the controller gains that place the closed loop poles at the desired locations under CC are N times larger than those under PAC, where N is the number of wedges. The results are applied to temperature stabilization of the fusing stage of a xerographic process.

No abstract