Equilibration of baroclinic instability in westward flows

We explore the dynamics of baroclinic instability in westward flows using an asymptotic weakly nonlinear model. The proposed theory is based on the multilayer quasi-geostrophic framework, which is reduced to a system governed by a single nonlinear prognostic equation for the upper layer. The dynamics of deeper layers are represented by linear diagnostic relations. A major role in the statistical equilibration of baroclinic instability is played by the latent zonally elongated modes. These structures form spontaneously in baroclinically unstable systems and effectively suppress the amplification of primary unstable modes. Special attention is given to the effects of bottom friction, which is shown to control both linear and nonlinear properties of baroclinic instability. The reduced-dynamics model is validated by a series of numerical simulations.

Model reduction of unstable systems based on balanced truncation algorithm

Model reduction of a system is an approximation of a higher-order system to a lower-order system while the dynamic behavior of the system is almost unchanged. In this paper, we will discuss model order reduction (MOR) strategies for unstable systems, in which the method based on the balanced truncation algorithm will be focused on. Since each MOR algorithm has its strengths and weakness, practical applications should be suitable for each specific requirement. Simulation results will demonstrate the correctness of the algorithms.

2DOF IMC and Smith-Predictor-Based Control for Stabilised Unstable First Order Time Delayed Plants

The article brings a brief revision of the two-degree-of-freedom (2-DoF) internal model control (IMC) and the 2-DoF Smith-Predictor-based (SP) control of unstable systems. It shows that the first important reason for distinguishing between these approaches is the limitations of the control action. However, it also reminds that, in addition to the seemingly lucrative dynamics of transients, the proposed approaches can conceal a tricky behavior with a structural instability, which may manifest itself only after a longer period of time. Instead, as one of possible reliable alternatives, two-step IMC and filtered Smith predictor (FSP) design are applied to unstable first-order time-delayed (UFOTD) systems. Firstly, the 2-DoF P controller yielding a double real dominant closed loop pole is applied. Only then the 2-DoF IMC or FSP controllers are designed, providing slightly slower, but more robust transients. These remain stable even in the long run, while also showing increased robustness.

Behavioral planning: Improving behavioral design with “roughly right” foresight

Many challenges emerging from the current COVID-19 pandemic are behavioral in nature, which has prompted the field of behavioral design to propose solutions for issues as wide-ranging as hand-washing, wearing masks, and the adoption of new norms for staying and working from home. On the whole, however, these behavioral interventions have been somewhat underwhelming, exposing an inherent brittleness that comes from three common “errors of projection” in current behavioral design methodology: projected stability, which insufficiently plans for the fact that interventions often function within inherently unstable systems; projected persistence, which neglects to account for changes in those system conditions over time; and projected value, which assumes that definitions of success are universally shared across contexts. Borrowing from strategic design and futures thinking, a new proposed strategic foresight model—behavioral planning—can help practitioners better address these system-level, anticipatory, and contextual weaknesses by more systematically identifying potential forces that may impact behavioral interventions before they have been implemented. Behavioral planning will help designers more effectively elicit signals indicating the emergence of forces that may deform behavioral interventions in emergent COVID-19 contexts, and promote “roughly right” directional solutions at earlier stages in solution development to better address system shifts.