S. Torkel Glad

Resolving actuator redundancy-optimal control vs. control allocation

This paper considers actuator redundancy management for a class of overactuated nonlinear systems. Two tools for distributing the control effort among a redundant set of actuators are optimal control design and control allocation. In this paper, we investigate the relationship between these two design tools when the performance indexes are quadratic in the control input. We show that for a particular class of nonlinear systems, they give exactly the same design freedom in distributing the control effort among the actuators. Linear quadratic optimal control is contained as a special case. A benefit of using a separate control allocator is that actuator constraints can be considered, which is illustrated with a flight control example.

Flight Control Design using Backstepping

Todays prevailing nonlinear design method for aircraft flight control is feedback linearization. This paper presents a new method to deal with the nonlinear aerodynamic forces and moments acting on ...

A backstepping design for flight path angle control

A nonlinear approach to flight path angle control is presented. Using backstepping, a globally stabilizing control law is derived. Although the nonlinear nature of the lift force is considered, the pitching moment to be produced is only linear in the measured states. Thus, the resulting control law is much simpler than if feedback linearization had been used. The free parameters that spring from the backstepping design are used to achieve a desired linear behavior around the operating point.A nonlinear approach to flight path angle control is presented. Using backstepping, a globally stabilizing control law is derived. Although the nonlinear nature of the lift force is considered, the pitching moment to be produced is only linear in the measured states. Thus, the resulting control law is much simpler than if feedback linearization had been used. The free parameters that spring from the backstepping design are used to achieve a desired linear behavior around the operating point.

Mass and Information Feedbacks through Receptor Endocytosis Govern Insulin Signaling as Revealed Using a Parameter-free Modeling Framework

Insulin and other hormones control target cells through a network of signal-mediating molecules. Such networks are extremely complex due to multiple feedback loops in combination with redundancy, shared signal mediators, and cross-talk between signal pathways. We present a novel framework that integrates experimental work and mathematical modeling to quantitatively characterize the role and relation between co-existing submechanisms in complex signaling networks. The approach is independent of knowing or uniquely estimating model parameters because it only relies on (i) rejections and (ii) core predictions (uniquely identified properties in unidentifiable models). The power of our approach is demonstrated through numerous iterations between experiments, model-based data analyses, and theoretical predictions to characterize the relative role of co-existing feedbacks governing insulin signaling. We examined phosphorylation of the insulin receptor and insulin receptor substrate-1 and endocytosis of the receptor in response to various different experimental perturbations in primary human adipocytes. The analysis revealed that receptor endocytosis is necessary for two identified feedback mechanisms involving mass and information transfer, respectively. Experimental findings indicate that interfering with the feedback may substantially increase overall signaling strength, suggesting novel therapeutic targets for insulin resistance and type 2 diabetes. Because the central observations are present in other signaling networks, our results may indicate a general mechanism in hormonal control.

Step Responses of Nonlinear Non-Minimum Phase Systems

For nonlinear systems, instability of the zero dynamics is known to correspond to the non-minimum phase property of linear systems. For linear systems it is also known that non-minimum phase is associated with certain step response behavior e.g. the initial direction of the step response is opposite to the final value. The corresponding step response properties of nonlinear systems are investigated in this contribution. It is also investigated whether a certain nonlinear canonical form gives insight into the relation between step response and non-minimum phase behavior.

Computing the Settling Time for Nonlinear Step Responses

The settling time for the step response of a nonlinear system can be computed using the Poincare-Dulac normal form. It is then possible to use a simple approximate formula, whose error can be estimated. The data needed can all be calculated from the leading coefficients of series expansions of the Poincare-Dulac transformation and the equilibrium curve.

Dealing with Inequalities in Polynomial Models

Abstract It is described how set membership identification and model rejection for polynomial models can be described using polynomial inequalities and inequations. Using difference algebra methods these problems can be reduced form based on so called autoreduced sets. It is shown that these descriptions generalize state space descriptions. It is also discussed how special forms of autoreduced sets can make methods based on interval methods easier to implement.

Technical Communique: Bounds on the response time under control constraints

We consider the problem of transferring the output of a linear system from one equilibrium value to another under control amplitude constraint. It is possible to give a simple lower bound on the time required, expressed in the longest time constant, the gain of the system, the change in y and the control bound. This theoretical bound appears to be useful as a practical lower bound of the rise time.