Jeffrey T. Scruggs

Design and experimental characterization of an electromagnetic transducer for large-scale vibratory energy harvesting applications

This article reports on the design and experimental characterization of an electromagnetic transducer for energy harvesting from large structures (e.g., multistory buildings and bridges), for which the power levels can be above 100 W and disturbance frequencies below 1 Hz. The transducer consists of a back-driven ballscrew coupled to a permanent-magnet synchronous machine with power harvesting regulated via control of a four-quadrant power electronic drive. Design considerations between various subsystems are illustrated and recommendations in terms of minimal values are made for each design metric. Developing control algorithms to take full advantage of the unique features of this type of transducer requires a mechanical model that can adequately characterize the device’s intrinsic nonlinear behavior. A new model is proposed that can effectively capture this behavior. Comparison with experimental results verifies that the model is accurate over a wide range of operating conditions. As such, the model can be used to assess the viability of the technology and to correctly design controllers to maximize power generation. To demonstrate the device’s energy harvesting capability, impedance matching theory is used to optimize the power generated from a base-excited tuned mass damper. Both theoretical and experimental investigations are compared and the results are shown to match closely.

Design of electromagnetic energy harvesters for large-scale structural vibration applications

This paper reports on the design and experimental validation of transducers for energy harvesting from largescale civil structures, for which the power levels can be above 100W, and disturbance frequencies below 1Hz. The transducer consists of a back-driven ballscrew, coupled to a permanent-magnet synchronous machine, and power harvesting is regulated via control of a four-quadrant power electronic drive. Design tradeoffs between the various subsystems (including the controller, electronics, machine, mechanical conversion, and structural system) are illustrated, and an approach to device optimization is presented. Additionally, it is shown that nonlinear dissipative behavior of the electromechanical system must be properly characterized in order to assess the viability of the technology, and also to correctly design the matched impedance to maximize harvested power. An analytical expression for the average power generated across a resistive load is presented, which takes the nonlinear dissipative behavior of the device into account. From this expression the optimal resistance is determined to maximize power for an example in which the transducer is coupled to base excited tuned mass damper (TMD). Finally, the results from the analytical model are compared to an experimental system that uses hybrid testing to simulated the dynamics of the TMD.

Optimization of partial-state feedback for vibratory energy harvesters subjected to broadband stochastic disturbances

In many applications of vibratory energy harvesting, the external disturbance is most appropriately modeled as a broadband stochastic process. Optimization of the average power generated from such disturbances is a feedback control problem, and solvable via LQG (linear–quadratic–Gaussian) control theory. Implementing the optimal feedback controller requires a power electronic drive capable of two-way power flow, which can impose dynamic relationships between the voltage and current of the transducer. Determining the optimal energy harvesting current control is accomplished by solving a nonstandard Riccati equation. In this paper we show that appropriate tuning of the passive parameters in the harvesting system results in a decoupled solution to the Riccati equation and a corresponding controller that only requires half of the states for feedback. However, even when such tuning methods are not used and the solution to the Riccati equation does not decouple, it is possible to determine the states in the feedback law that contribute the most to the average power generated by the harvester. As such, partial-state feedback gains can be optimized using a gradient descent method. Two energy harvesting examples are presented, including a single-degree-of-freedom oscillator with an electromagnetic actuator and a piezoelectric bimorph cantilever beam, to demonstrate these concepts.

Multi-objective nonlinear control of semiactive and regenerative systems

Many modern structural control devices for earthquake engineering applications are essentially passive devices with adaptive parameters. Semiactive and regenerative forcing systems are two examples. In order to achieve performance superior to time-invariant passive systems, these devices must be controlled in the nonlinear regime, and consequently it is nontrivial to develop feedback controllers which adhere to analytically-computable measures of closed-loop performance. In the context of stationary random vibration, current state-of-the-art control design methods do not guarantee to simultaneously keep the variances of a set of important structural response quantities below desired thresholds. In this paper, a generalized control design approach is presented which guarantees bounds on the variances of multiple response quantities. The method is illustrated through simulation of a six-story, base isolated structure, with two control devices. Both semiactive and regenerative designs are considered in this example.

Robust stochastic design of linear controlled systems for performance optimization

This study discusses a robust controller synthesis methodology for linear, time invariant systems, under probabilistic parameter uncertainty. Optimization of probabilistic performance robustness for [script H]_2 and multi-objective [script H]_2 measures is investigated, as well as for performance measures based on first-passage system reliability. The control optimization approaches proposed here exploit recent advances in stochastic simulation techniques. The approach is illustrated for vibration response suppression of a civil structure. The results illustrate that, for problems with probabilistic uncertainty, the explicit optimization of probabilistic performance robustness can result in markedly different optimal feedback laws, as well as enhanced performance robustness, when compared to traditional “worst-case” notions of robust optimal control.

Probabilistically-robust performance optimization for controlled linear stochastic systems

This study discusses a robust controller synthesis methodology for linear time invariant systems characterized by probabilistic parameter uncertainty. The optimization of the robust performance is considered. The extension of pre-existing, synthesis approaches, such as multi-objective H2 design, to account for probabilistic uncertainty is investigated. A design based on the concept of the reliability of the system response output is also considered. Analysis and synthesis methodologies based on stochastic simulation techniques are discussed. The design approach is applied in a structural control example. The results illustrate the differences between the various probabilistic performance objectives and the importance of adopting a probabilistic characterization for model uncertainty when compared to nominal design or to the design using a worst-case scenario approach.

Analysis and synthesis of self-powered linear structural control with imperfect energy storage

Self-powered vibration control systems are characterized by a distributed network of regenerative force actuators, which are interfaced with a common power bus. Also connected to the power bus is an energy-storing subsystem, such as a supercapacitor, flywheel, or battery. The entire system is controlled using switch-mode power electronics, and the only power required for system operation is that necessary to perform these switching operations. The resultant energy conservation constraint restricts the set of feedback laws that are feasible. This paper reports on an LMI feasibility constraint for linear self-powered feedback laws, in terms of actuator and storage hardware parameters. Two design applications of this constraint are illustrated. The first is the determination of the least-efficient energy storage parameters necessary to realize a given passive control law. It is shown that this problem is quasiconvex, and may be posed as a generalized eigenvalue problem. The second example uses an extension of positive-real-constrained H2 optimal control, to optimize a control law subject to the feasibility constraint. Both examples are illustrated in the context of base-excited vibrating structures, subjected to stationary stochastic excitation.

Optimization of power generation from energy harvesters in broadband stochastic response

This paper presents recent analytical results pertaining to the optimization of power flow from vibratory energy harvesting systems, using principles from optimal feedback control and network theory. Historically, much of the research concerning such technologies has presumed that the vibratory energy source, from which power is to be extracted, oscillates harmonically at a known frequency. In this case, the optimization of power extraction from such sources by a resonant energy harvester can readily be accomplished through the use of classical impedance matching techniques. However, in many applications, vibratory power sources exhibit dynamic behavior more appropriately characterized by a stochastic process. In some cases, the power spectrum of this process may exhibit a rather wide band. In such circumstances, impedance matching techniques cannot be used to optimize power flow from the harvester, because the dynamic impedance they prescribe is always anticausal. This paper presents several theoretical concepts, intended for broad application in the energy harvesting area, which can be used to optimize power extracted from broadband sources. It is shown that in the broadband case, an optimal causal impedance still exists which maximizes power generation, but in order to derive it, the dissipation in the electrical system, as well as the mechanical system, must be taken into account in the system model. Levels of power generation with this controller are compared to those of the anticausal optimal performance, as well as to control design techniques that match the anticausal impedance at the resonant frequency. It is demonstrated that such causal matching techniques can be significantly sub-optimal in broadband applications, especially when electronic conversion is relatively efficient.

Peak-gain-bounded design of constrained controllable damping in vibrating structures

This paper concerns the design of mechanical vibration suppression systems with controllable mechanical damping. For such systems, the paper illustrates techniques for both linear and nonlinear damping design, which place an upper bound on the peak gain from the structural disturbances to response performance outputs. The technique is an extension of many Lyapunov-based damping techniques in the open literature on semiactive systems. Presently, such techniques admit performance measures which depend only on the system state. This paper discusses theoretical extensions to those methods to accommodate performance measures which are explicitly dependent on the external disturbance and control forces. The theory is illustrated via simulation of a base-excited structure equipped with viscous, semiactive, or regenerative damping systems, with the objective of minimizing the peak gain from the base acceleration amplitude to the vector of inter-story drifts and structural accelerations.

Nonlinear stochastic feedback controllers for vibratory energy harvesters with power flow constraints

This study addresses the formulation of feedback controllers for stochastically-excited vibratory energy harvesters. Maximizing power generation from stochastic disturbances can be accomplished using LQG control theory, with the transducer current treated as the control input. For the case where the power flow direction is unconstrained, an electronic drive capable of extracting as well as delivering power to the transducer is required to implement the optimal controller. It is demonstrated that for stochastic disturbances characterized by second-order, bandpass-filtered white noise, energy harvesters can be passively tuned such that optimal stationary power generation only requires half of the system states for feedback in the active circuit. However, there are many applications where the implementation of a bi-directional power electronic drive is infeasible, due to the higher parasitic losses they must sustain. If the electronics are designed to be capable of only single-directional power flow (i.e., where the electronics are incapable of power injection), then these parasitics can be reduced significantly, which makes single-directional converters more appropriate at smaller power scales. The constraint on the directionality of power flow imposes a constraint on the feedback laws that can be implemented with such converters. In this paper, we present a sub-optimal nonlinear control design technique for this class of problems, which exhibits an analytically computable upper bound on average power generation.Copyright