Tuhin Das

Swing-Up Control of the Pendubot: An Impulse–Momentum Approach

The standard control problem of the pendubot refers to the task of stabilizing its equilibrium configuration with the highest potential energy. Linearization of the dynamics of the pendubot about this equilibrium results in a completely controllable system and allows a linear controller to be designed for local asymptotic stability. For the underactuated pendubot, the important task is, therefore, to design a controller that will swing up both links and bring the configuration variables of the system within the region of attraction of the desired equilibrium. This paper provides a new method for swing-up control based on a series of rest-to-rest maneuvers of the first link about its vertically upright configuration. The rest-to-rest maneuvers are designed such that each maneuver results in a net gain in energy of the second link. This results in swing-up of the second link and the pendubot configuration reaching the region of attraction of the desired equilibrium. A four-step algorithm is provided for swing-up control followed by stabilization. Simulation results are presented to demonstrate the efficacy of the approach.

Robust Control of Solid Oxide Fuel Cell Ultracapacitor Hybrid System

Mitigating fuel starvation and improving load-following capability of solid oxide fuel cells (SOFC) are conflicting control objectives. In this paper, we address this issue using a hybrid SOFC ultracapacitor configuration. Fuel starvation is prevented by regulating the fuel cell current using a steady-state invariant relationship involving fuel utilization, fuel flow, and current. Two comprehensive control strategies are developed. The first is a Lyapunov-based nonlinear control and the second is a standard H∞ robust control. Both strategies additionally control the state of charge of the ultracapacitor that provides transient power compensation. A hardware-in-the-loop test stand is developed where the proposed control strategies are verified.

Technical communique: Optimally switched linear systems

In this paper we address the problem of optimal switching for switched linear systems. The uniqueness of our approach lies in describing the switching action by multiple control inputs. This allows us to embed the switched system in a larger family of systems and apply Pontryagins Minimum Principle for solving the optimal control problem. This approach imposes no restriction on the switching sequence or the number of switchings. This is in contrast to search based algorithms where a fixed number of switchings is set a priori. In our approach, the optimal solution can be determined by solving the ensuing two-point boundary value problem. Results of numerical simulations are provided to support the proposed method.

Exponential stabilization of the rolling sphere

In this paper we present a non-smooth controller for exponential stabilization of the sphere. This has remained an open problem despite significant progress in nonholonomic systems. Our control design is based on inputs in a rotating coordinate frame that individually produce primitive motions of the sphere along straight lines and circular arcs. The rotating coordinate frame is chosen in concert with Euler angle description of orientation and placement of the desired configuration at the singularity of the representation. In our paper, we separately establish global stability of the desired configuration and exponential convergence. Our theoretical claims are validated through numerical simulations.

Reconfiguration of a rolling sphere: A problem in evolute-involute geometry

This paper provides a new perspective to the problem of reconfiguration of a rolling sphere. It is shown that the motion of a rolling sphere can be characterized by evolute-involute geometry. This characterization, which is a manifestation of our specific selection of Euler angle coordinates and choice of angular velocities in a rotating coordinate frame, allows us to recast the three-dimensional kinematics problem as a problem in planar geometry. This, in turn, allows a variety of optimization problems to be defined and admits infinite solution trajectories. It is shown that logarithmic spirals form a class of solution trajectories and they result in exponential convergence of the configuration variables.

Adaptive Control of a Solid Oxide Fuel Cell Ultra-Capacitor Hybrid System

Solid oxide fuel cells (SOFCs) offer a number of advantages beyond those of most other fuel cells. However, like other fuel cells, rapid load following is difficult, and can lead to fuel starvation and consequently fuel cell damage. Mitigating fuel starvation and improving load following capabilities are conflicting control objectives. However, the issue can be addressed by the hybridization of the system with an energy storage device. In this paper, a steady-state property of the SOFC, combined with a current regulation strategy, is used to manage transient fuel utilization and thereby address fuel starvation. Meanwhile, an overall system strategy is employed to manage energy sharing in the hybrid system for load following as well as for maintaining the state-of-charge of the energy storage device. This work presents an adaptive control algorithm that uses online parameter estimation to update the controller. The control design is validated on a hardware-in-the-loop setup and experimental results are provided.

Steady-State and Transient Analysis of a Steam-Reformer Based Solid Oxide Fuel Cell System

In this paper we perform a model-based analysis of a solid oxide fuel cell (SOFC) system with an integrated steam reformer and with methane as a fuel. The objective of this study is to analyze the steady-state and transient characteristics of this system. For the analysis, we develop a detailed control-oriented model of the system that captures the heat and mass transfer, chemical kinetics, and electrochemical phenomena. We express the dynamics of the reformer and the fuel cell in state-space form. By applying coordinate transformations to the state-space model, we derive analytical expressions of steady-state conditions and transient behaviors of two critical performance variables, namely, fuel utilization and steam-to-carbon balance. Using these results, we solve a constrained steady-state fuel optimization problem using linear programming. Our analysis is supported by simulations. The results presented in this paper can be applied in predicting steady-state conditions and certain transient behaviors and will be useful in control development for SOFC systems.

Experimental study of a planar atmospheric-pressure plasma operating in the microplasma regime

Electrical characterization of a nonthermal radio-frequency atmospheric-pressure microplasma in a parallel plate configuration has shown that reducing electrode gap into the submillimeter range increases current and power density at a reduced voltage as compared to similar plasmas at larger electrode gaps which have no gap dependence. Calculation of sheath thickness and electric fields in the sheath and in the bulk demonstrate a dependence on the electrode gap as it is reduced into the submillimeter regime, indicating a distinct regime of operation.

Optimal trajectory planning for hot-air balloons in linear wind fields

The altitude of hot-air balloons is controlled by heating the air trapped inside the balloon and allowing the air to cool naturally. Apart from controlling the altitude, it is desirable to utilize the wind e eld to position the balloon at a target location while minimizing fuel consumption. This can be posed as an optimal control problem with free end states, where the heat input to the system is the control variable. The problem is intractable because of the switching nature of the heat input and highly nonlinear state equations derived from the thermodynamic model of the balloon. In this paper we address the optimal control problem within a space of a few kilometers where we assume the wind e elds to be known and linear. We simplify the dynamic model of the balloon and obtain optimal trajectories to the target location by solving a two-point boundary-value problem. By ree ning the simplie ed dynamic model, the accuracy of the optimal trajectories are improved to match well with trajectories obtained using the nonlinear model. Our approach based on simplie cation of the balloon dynamic model enables us to solve the intractable nonlinear optimal control problem and provides insight into the optimal trajectories, such as numberof switchings of input and loss of accuracy for specie c wind proe les. Except for these specie c wind proe les, our approach yields accurate trajectories for the balloon and providesa solution to an important problem that has not been adequately addressed in the literature.

Shared-Sensing and Control Using Reversible Transducers

As an alternative to self-sensing, we propose the concept of shared-sensing for reversible transducers. In shared-sensing, reversible transducers are continuously switched between actuator and sensor modes. This results in a hybrid system, and, in this paper, we investigate stability properties of the equilibrium for linear systems and a class of nonlinear systems with a single shared-sensing transducer. Our theoretical results are validated through simulations and experiments with a dc servo motor.