Saeid Bashash

Robust Multiple Frequency Trajectory Tracking Control of Piezoelectrically Driven Micro/Nanopositioning Systems

A novel modeling and control methodology is proposed in this paper for real-time compensation of nonlinearities along with precision trajectory control of piezoelectric actuators in various range of frequency operation. By integrating a modified Prandtl-Ishlinskii hysteresis operator with a second-order linear dynamics, a nonlinear dynamic model and an inverse feedforward controller are developed and experimentally validated for a piezoelectrically driven nanopositioning stage. This modeling and control framework, however, lacks the accuracy due to the hysteresis model limitation, parametric uncertainties, and ever present unmodeled dynamics. Utilizing the sliding mode control strategy coupled with a perturbation estimation technique, a robust controller is then proposed for trajectory tracking of the actuator displacement. The controller gains are adjusted based on an intelligent comparison of the dynamic model and the control law. Eventually, the performance of the proposed controller is verified for the nanopositioning stage which is equipped with a high resolution capacitive position sensor. Experimental results demonstrate that the controller is capable of precisely tracking triangular and multiple frequency sinusoidal trajectories, which are common practices in many scanning probe microscopy systems.

Robust Adaptive Control of Coupled Parallel Piezo-Flexural Nanopositioning Stages

Precision control of multiple-axis piezo-flexural stages used in a variety of scanning probe microscopy systems suffers not only from hysteresis nonlinearity, but also from parametric uncertainties and the cross-coupled motions of their axes. Motivated by these shortfalls, a Lyapunov-based control strategy is proposed in this article for simultaneous multiple-axis tracking control of piezo-flexural stages. A double-axis stage is considered for system analysis and controller validation. Hysteresis and coupling nonlinearities are studied through a number of experiments, and it is demonstrated that the widely used proportional-integral (PI) controller lacks accuracy in high-frequency tracking. Adopting the variable structure control method, a robust adaptive controller is then derived with its stability guaranteed through the Lyapunov criterion. It is shown that a parallelogram-type zone of attraction can be explicitly formed for the closed-loop system to which the error phase trajectory converges. Practical implementation of the controller demonstrates effective double-axis tracking control of the stage in the presence of hysteresis and coupling nonlinearities and despite parametric uncertainties for low-and high-frequency trajectories. Moreover, good agreements are achieved between the experiments and theoretical developments.

Reduction of an Electrochemistry-Based Li-Ion Battery Model via Quasi-Linearization and Padé Approximation

This paper examines an electrochemistry-based lithium-ion battery model developed by Doyle, Fuller, and Newman. The paper makes this model more tractable and conducive to control design by making two main contributions to the literature. First, we adaptively solve the models algebraic equations using quasi-linearization. This improves the models execution speed compared to solving the algebraic equations via optimization. Second, we reduce the models order by deriving a family of analytic Pade approximations to the models spherical diffusion equations. The paper carefully compares these Pade approximations to other published methods for reducing spherical diffusion equations. Finally, the paper concludes with battery simulations showing the significant impact of the proposed model reduction approach on the battery models overall accuracy and simulation speed.

Modeling and Control of Aggregate Air Conditioning Loads for Robust Renewable Power Management

This paper examines the problem of demand-side energy management in smart power grids through the setpoint control of aggregate thermostatic loads. This paper models these loads using a novel partial differential equation framework that builds on existing diffusion- and transport-based load modeling ideas in the literature. Both this partial differential equation (PDE) model and its finite-difference approximations are bilinear in the state and control variables. This key insight creates a unique opportunity for designing nonlinear load control algorithms with theoretically guaranteed Lyapunov stability properties. This papers main contribution to the literature is the development of the bilinear PDE model and a sliding mode controller for the real-time management of thermostatic air conditioning loads. The proposed control scheme shows promising performance in adapting aggregate air conditioning loads to intermittent wind power.

Modeling and control insights into demand-side energy management through setpoint control of thermostatic loads

This paper examines the problem of using thermostat offset signals to directly control distributed air conditioning loads attached to the grid. The paper models these loads using a novel partial differential equation framework that builds on existing diffusion- based load modeling ideas in the literature. Both this PDE model and its finite-difference discretizations are bilinear in the state and control variables. This key insight creates a unique opportunity for designing nonlinear direct load control algorithms with theoretically guaranteed Lyapunov stability properties. The papers main contribution to the literature is the development of the bilinear PDE model and Lyapunov- stable controller for real-time management of thermostatic air conditioning loads.

Modeling and experimental vibration analysis of nanomechanical cantilever active probes

Nanomechanical cantilever (NMC) active probes have recently received increased attention in a variety of nanoscale sensing and measurement applications. Current modeling practices call for a uniform cantilever beam without considering the intentional jump discontinuities associated with the piezoelectric layer attachment and the NMC cross-sectional step. This paper presents a comprehensive modeling framework for modal characterization and dynamic response analysis of NMC active probes with geometrical discontinuities. The entire length of the NMC is divided into three segments of uniform beams followed by applying appropriate continuity conditions. The characteristics matrix equation is then used to solve for system natural frequencies and mode shapes. Using an equivalent electromechanical moment of a piezoelectric layer, forced motion analysis of the system is carried out. An experimental setup consisting of a commercial NMC active probe from Veeco and a state-of-the-art microsystem analyzer, the MSA-400 from Polytec, is developed to verify the theoretical developments proposed here. Using a parameter estimation technique based on minimizing the modeling error, optimal values of system parameters are identified. Mode shapes and the modal frequency response of the system for the first three modes determined from the proposed model are compared with those obtained from the experiment and commonly used theory for uniform beams. Results indicate that the uniform beam model fails to accurately predict the actual system response, especially in multiple-mode operation, while the proposed discontinuous beam model demonstrates good agreement with the experimental data. Such detailed and accurate modeling framework can lead to significant enhancement in the sensitivity of piezoelectric-based NMC sensors for use in variety of sensing and imaging applications.

Transport-Based Load Modeling and Sliding Mode Control of Plug-In Electric Vehicles for Robust Renewable Power Tracking

This paper develops a modeling and control paradigm for the aggregate charging dynamics of plug-in electric vehicles (PEVs). The central goal of the paper is to derive a control policy that can adapt the aggregate charging power of PEVs to highly intermittent renewable power. The key assumption here is that the grid is able to directly control the charging power of PEVs in real-time, through broadcasting a universal control signal. Using the transport-based load modeling principle, we develop a partial differential equation model for the collective charging of PEVs. We use real driving data to simulate the model and validate it against a PEV Monte Carlo simulation model. Adopting the sliding mode control theory, we then develop a robust output tracking controller for the system. The controller uses the real-time error between power supply and demand as the only measured signal, and attempts to suppress it despite the variation of the population of PEVs on the grid. We examine the performance of the controller using numerical simulations on a real wind power trajectory.

Optimal Control of Film Growth in Lithium-Ion Battery Packs via Relay Switches

Recent advances in lithium-ion battery modeling suggest unequal but controlled and carefully timed charging of individual cells by reduce degradation. This paper compares anode-side film formation for a standard equalization scheme versus unequal charging through switches that are controlled by deterministic dynamic programming (DDP) and DDP-inspired heuristic algorithms. A static map for film growth rate is derived from a first-principles battery model adopted from the electrochemical engineering literature. Using this map, we consider two cells that are connected in parallel via relay switches. The key results are the following: 1) optimal unequal and delayed charging indeed reduces film buildup, and 2) a near-optimal state feedback controller can be designed from the DDP solution and film growth rate convexity properties. The simulation results indicate that the heuristic state feedback controller achieves near optimal performance relative to the DDP solution, with significant reduction in film growth compared to charging both cells equally, for several film growth models. Moreover, the algorithms achieve similar film reduction values on the full electrochemical model. These results correlate with the convexity properties of the film growth map. Hence, this paper demonstrates that unequal charging may indeed reduce film growth, given certain convexity properties exist, lending promise to the concept for improving battery pack life.

Charge trajectory optimization of plug-in hybrid electric vehicles for energy cost reduction and battery health enhancement

This paper examines the problem of optimizing the charge trajectory of a plug-in hybrid electric vehicle (PHEV), defined as the timing and rate with which the PHEV obtains electricity from the power grid. Two objectives are considered in this optimization. First, we minimize the total cost of fuel and electricity consumed by the PHEV over a 24-hour naturalistic drive cycle. We predict this cost using a previously-developed stochastic optimal PHEV power management strategy. Second, we also minimize total battery health degradation over the course of the 24-hour cycle. This degradation is predicted using an electrochemistry-based model of anode-side resistive film formation in Li-ion batteries. The paper shows that these two objectives are conflicting, and trades them off using a non-dominated sort genetic algorithm, NSGA-II. As a result, a Pareto front of optimal PHEV charge trajectories is obtained. The effects of electricity price and trip schedule on the Pareto front are analyzed and discussed.

Robust demand-side plug-in electric vehicle load control for renewable energy management

Plug-in electric vehicles can provide the power grid with some degree of control authority over fluctuations in electric load, thanks to their charging flexibility. The magnitude of this control authority depends on a variety of factors including the number of vehicles plugged into the grid, their instantaneous power demands, and the degree of flexibility in these demands. This paper addresses the problem of using a universally broadcast control signal to directly control the charge rate of a fleet of plug-in electric vehicles connected to the grid. The paper specifically seeks a control algorithm that is robust to uncertainties in renewable energy generation and the number of grid-connected vehicles. We adopt the sliding mode control strategy to achieve stability and robustness with respect to the collective effects of system uncertainties. The control law and robustness conditions are derived using the Lyapunov stability criterion. The paper shows that using only the real-time imbalance between the electricity supply and demand as a measured system output, the controller is able to precisely attenuate this imbalance, achieving reliable demand-side load management. Numerical simulations are provided to evaluate the performance of this controller.