A bode sensitivity integral for linear time-periodic systems

Bode's sensitivity integral is a well-known formula that quantifies some of the limitations in feedback control for linear time-invariant systems. In this note, we show that there is a similar formula for linear time-periodic systems. The harmonic transfer function is used to prove the result. We use the notion of roll-off 2, which means that the first time-varying Markov parameter is equal to zero. It then follows that the harmonic transfer function is an analytic operator and a trace class operator. These facts are used to prove the result.     

Feedback–Feedforward Scheduling of Control Tasks

A scheduling architecture for real-time control tasks is proposed. The scheduler uses feedback from execution-time measurements and feedforward from workload changes to adjust the sampling periods of the control tasks so that the combined performance of the controllers is optimized. The performance of each controller is described by a cost function. Based on the solution to the optimal resource allocation problem, explicit solutions are derived for linear and quadratic approximations of the cost functions. It is shown that a linear rescaling of the nominal sampling frequencies is optimal for both of these approximations. An extensive inverted pendulum example is presented, where the performance obtained with open-loop, feedback, combined feedback and feedforward scheduling, and earliest-deadline first scheduling are compared. The performance under earliest-deadline first scheduling is explained by studying the behavior of periodic tasks under overload conditions. It is shown that the average values of the sampling periods equal the nominal periods, rescaled by the processor utilization.     

Using an optimised OSL single-aliquot regenerative-dose protocol for low-dose retrospective dosimetry on household salt

The single-aliquot regenerative-dose (SAR) protocols used in retrospective dosimetry for optically stimulated luminescence measurements have been mainly developed for archaeological and geological dating of quartz and feldspar. The aim in this study is to find a read-out protocol that can generate the most reproducible signal for household salt (NaCl) at absorbed doses below 100 mGy. The relation between the reproducibility of the signal, in terms of the ratio between given absorbed dose and SAR-calculated dose, and parameters such as test-dose pre-heat temperature has been studied. It was found that a temperature of 200 °C yielded the best reproducibility in the SAR-calculated dose, which is a somewhat higher pre-heat temperature than what is used for dating of quartz.     

Measurements of long-term external and internal radiation exposure of inhabitants of some villages of the Bryansk region of Russia after the Chernobyl accident

A Nordic-Soviet programme was initiated in 1990 to evaluate the external and internal radiation exposure of the inhabitants of several villages in the Bryansk region of Russia. This area was one of the number of areas particularly affected by the nuclear accident at the Chernobyl Nuclear Power Plant in 1986. Measurements were carried out yearly until 1998 and after that more irregularly; in 2000, 2006 and 2008 respectively. The effective dose estimates were based on individual thermoluminescent dosemeters and on in vivo measurements of the whole body content of ¹³⁷Cs (and ¹³⁴Cs during the first years of the programme). The decrease in total effective dose during the almost 2 decade follow-up was due to a continuous decrease in the dominating external exposure and a less decreasing but highly variable exposure from internal irradiation. In 2008, the observed average effective dose (i.e. the sum of external and internal exposure) from Chernobyl ¹³⁷Cs to the residents was estimated to be 0.3 mSv y⁻¹. This corresponds to 8% of the estimated annual dose in 1990 and to 1% of the estimated annual dose in 1986. As a mean for the population group and for the period of the present study (2006-2008), the average yearly effective dose from Chernobyl cesium was comparable to the absorbed dose obtained annually from external exposure to cosmic radiation plus internal exposure to naturally occurring radionuclides in the human body. Our data indicate that the effective dose from internal exposure is becoming increasingly important as the body burdens of Chernobyl ¹³⁷Cs are decreasing more slowly than the external exposure. However, over the years there have been large individual variations in both the external and internal effective doses, as well as differences between the villages investigated. These variations and differences are presented and discussed in this paper.     

Comments on “Mixed L∞/H∞suboptimal controllers for SISO continuous time systems”

The authors state that they have no serious criticism of the original paper but make certain remarks. An example in the original illustrates a method to do tradeoffs between two design goals: H_∞ and L^∞. To make a fair comparison, they authors say that the optimal H_∞ norm should have been presented. The also point out misprints, and make remarks on the cancellation of the integrator pole and the tending to ∞ of the settling time     

On the notion of strong stabilizability

A system is called strongly stabilizable (SS) if it can be stabilized using a stable controller. Observer state feedback can be used to design a controller of the same order as the system, but the designs may lead to unstable controllers. The implementation of an unstable controller should be done with care and with a well-designed safety net. One implementation could use a stable observer fed with actual input in addition to the measured output. Several examples are discussed, and how unstable controllers might be required for good closed-loop performance, even if they are not required for stability is shown     

Frequency-domain analysis of linear time-periodic systems

In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature.     

LQR optimization of linear system switching

Considers offline optimization of a switching sequence for a given finite set of linear control systems, together with joint optimization of control laws. A linear quadratic full information criterion is optimized and dynamic programming is used to find an optimal switching sequence and control law. The main result is a method for efficient pruning of the search tree to avoid combinatoric explosion. A method to prove optimality of a found candidate switch sequence and corresponding control laws is presented.     

Dual control of a first-order system with two possible gains

The dual control law for the system y(t + 1) = ay(t) + bu(t) + σe(t + 1) is computed. Here a is supposed to be known. The gain b is unknown but can only take two values, b₁ or b₂. The Bellman equation is solved numerically. Properties of the dual control law are discussed. By varying a it is studied how probing depends on stability. For small a there is no probing. It is shown that the area of probing is increased as the process becomes more unstable.