Hector Perez

Output tracking between operating points for nonlinear processes: Van de Vusse example

Inversion-based approach finds an input that exactly tracks a desired output trajectory-the method has been recently extended to nonlinear nonminimum phase systems using stable-inversion techniques. Exact-output tracking inputs can be found by the stable-inversion method provided the system can be maintained near (local to) an equilibrium point of the system. However, inversion for the nonlocal case is more challenging because inverse solutions may not exist, for example, when the equilibrium point (operating point) is changed. Such changes in operating points are necessary in process control applications, for example, during startups, shutdowns, and grade transitions. Nonlocal transfers of a system from one operating point to another operating point along prespecified output trajectories are studied in this article for the Van de Vusse example, which is a benchmark problem in nonlinear nonminimum-phase process-control.

Design and Control of Optimal Scan Trajectories: Scanning Tunneling Microscope Example

This article addresses the optimal (minimal input energy) design of scan trajectories, which is important in applications such as the imaging and manipulation of nano-scale surface phenomena using scanning tunneling microscopes (STM), MEMS-based microscanners, quick-return mechanisms and cams used in manufacturing, and general repeating processes. The contribution of this article is the systematic solution of the optimal scan-trajectory design problem. As opposed to existing techniques that require prespecification of the desired output trajectory (such prespecifications can be ad hoc), the optimal output trajectory is found as a result of the proposed input-energy minimization approach. In this sense, the proposed approach leads to a systematic solution of the optimal output-trajectory-design problem. The proposed optimal scanning method is applied to an experimental scanning tunneling microscope; simulation and experimental results are presented to illustrate the efficacy of the proposed approach to design optimal scan-trajectories.

Enhanced Performance of Li-Ion Batteries via Modified Reference Governors and Electrochemical Models

This paper examines reference governor (RG) methods for satisfying state constraints in Li-ion batteries. Mathematically, these constraints are formulated from a first principles electrochemical model. Consequently, the constraints explicitly model specific degradation mechanisms, such as lithium plating, lithium depletion, and overheating. This contrasts with the present paradigm of limiting measured voltage, current, and/or temperature. The critical challenges, however, are that: 1) the electrochemical states evolve according to a system of nonlinear partial differential equations, and 2) the states are not physically measurable. Assuming available state and parameter estimates, this paper develops RGs for electrochemical battery models. The results demonstrate how electrochemical model state information can be utilized to ensure safe operation, while simultaneously enhancing energy capacity, power, and charge speeds in Li-ion batteries.

BATTERY CHARGE CONTROL WITH AN ELECTRO-THERMAL-AGING COUPLING

Efficient and safe battery charge control is an important prerequisite for large-scale deployment of clean energy systems. This paper proposes an innovative approach to devising optimally health-conscious fast-safe charge protocols. A multi-objective optimal control problem is mathematically formulated via a coupled electro-thermal-aging battery model, where electrical and aging sub-models depend upon the core temperature captured by a two-state thermal sub-model. The Legendre-Gauss-Radau (LGR) pseudo-spectral method with adaptive multi-mesh-interval collocation is employed to solve the resulting highly nonlinear six-state optimal control problem. Charge time and health degradation are therefore optimally traded off, subject to both electrical and thermal constraints. Minimum-time, minimum-aging, and balanced charge scenarios are examined in detail. The implications of the upper voltage bound, ambient temperature, and cooling convection resistance to the optimization outcome are investigated as well.Copyright

Optimal output transitions for linear systems

Addresses the optimal output transition problem for linear systems. The goal is to transfer the system output from an initial value to a final output value with zero residual vibrations in the output. Such problems arise in the point-to-point positioning applications such as positioning of disk drive heads. Methods have been developed (previously) to achieve such output transition by constraining the internal states to be zero at the beginning and at the end of the output transition. The output transition problem is then solved as an optimal state transition problem. However, the output transition cost is not minimal. Output transition costs can be further reduced if the internal states are not constrained to be zero at the beginning and at the end of the output transition. The optimal output transition is posed and analytical solution is presented by (a) using the standard optimal state transition approach to obtain the control law during the output transition and then (b) integrating this with the inversion-based approach to find inputs that maintain perfect output tracking before the initiation and after the completion of the output transition by using pre- and post-actuation. An example system is studied and simulation results are presented to illustrate the performance improvement over approaches to point-to-point output transition, which do not use pre- and post-actuation.

Optimal Charging of Li-Ion Batteries With Coupled Electro-Thermal-Aging Dynamics

Fast and safe charging protocols are crucial for enhancing the practicality of batteries, especially for mobile applications, such as smartphones and electric vehicles. This paper proposes an innovative approach to devising optimally health-conscious fast-safe charge protocols. A multiobjective optimal control problem is mathematically formulated via a coupled electro-thermal-aging battery model, where electrical and aging submodels depend upon the core temperature captured by a two-state thermal submodel. The Legendre–Gauss–Radau pseudospectral method with adaptive multi-mesh-interval collocation is employed to solve the resulting highly nonlinear six-state optimal control problem. Charge time and health degradation are, therefore, optimally traded off, subject to both electrical and thermal constraints. Minimum-time, minimum-aging, and balanced charge scenarios are examined in detail. Sensitivities to the upper voltage bound, ambient temperature, and cooling convection resistance are investigated as well. Experimental results are provided to compare the tradeoffs between a balanced and traditional charge protocol.

Sensitivity-based interval PDE observer for battery SOC estimation

Complex multi-partial differential equation (PDE) electrochemical battery models are characterized by parameters that are often difficult to measure or identify. This parametric uncertainty influences the state estimates of electrochemical model-based observers for applications such as state-of-charge (SOC) estimation. This paper develops a sensitivity-based interval observer that maps bounded parameter uncertainty to state estimation intervals, within the context of electrochemical PDE models and SOC estimation. Theoretically, this paper extends the notion of interval observers to PDE models using a sensitivity-based approach. Practically, this paper quantifies the sensitivity of battery state estimates to parameter variations, enabling robust battery management schemes.

Minimum-energy output transitions for linear discrete-time systems: Flexible structure applications

This paper finds minimum-energy inputs to change the position of an output point, on a flexible structure, from one value to another. Current methods transform the output-transition problem into a state-to-state transition problem by constraining the initial and final states of the output transition, for example, to be rest (rigid-body) configurations of the flexible structure. However, the choice of the initial and final states can be ad hoc, and the resulting output-transition cost (input energy) might not be minimum. The contribution of this paper is the direct solution of the optimal output-transition problem; the problem is posed and solved for general linear discrete-time systems. The novelty of the proposed approach is that inputs are not applied just during the output-transition time interval; rather, inputs are also applied outside the output-transition time interval, that is, before the beginning of and after the end of the output-transition time interval. (These inputs are called pre- and postactuation.) The implications of using pre- and postactuation are illustrated by using an example of discrete-time flexible structure model, which consists of a flexible rod connecting two masses. Simulation results are presented, which show substantial reduction of output-transition costs with the use of the proposed method when compared to the use of the standard state-to-state transition approach.

Design and control of optimal feedforward trajectories for scanners: STM example

This article addresses the design and control of optimal scan trajectories, which is important in applications such as the imaging of nano-scale surface phenomena using scanning tunneling microscopes (STM), quick-return mechanisms and cam used in manufacturing, and general repeating processes. In this article we pose the problem of designing the output trajectory for a scanner such that the input energy is minimized. The problem is solved by first integrating optimal control techniques with a model-based inversion approach. After this integration, the input-energy for the entire scan is then minimized to solve the optimal scanning problem. Additionally, the method is applied to high-speed scanning of an STM, which is a key tool in emerging nanotechnologies. Simulation and experimental results are presented to illustrate the technique and its advantages.

Feedforward trajectory design for output transitions in discrete-time systems: disk-drive example

The article proposes a direct approach to solve the optimal (minimal input energy) output-transition problem for linear discrete-time systems. The goal is to transfer and maintain the output from an initial value (y(k) = y_ for all k /spl les/ k/sub i/) to a final value (y(k) = y~ for all k /spl ges/ k/sup f/) within a prescribed number of time steps (k/sub f/-k/sub i/). Previous methods solve this output-transition problem by transforming it into a state-transition problem, i.e., the initial and final states(/spl kappa/(k/sub i/) and /spl kappa/(k/sub f/), respectively) are chosen and a minimum-energy state-to-state transition problem is solved. However, the choice of the initial and final states can be ad hoc and the resulting output-transition cost (input energy) may not be minimal. In contrast, the contribution of this article is the solution of the optimal output-transition problem for linear discrete-time systems. Example discrete-time model of a disk-drive servo system is studied to illustrate the proposed method. Simulation results show substantial reduction of transition costs with the use of the proposed method when compared to the use of approaches that are based on minimum-energy state transitions.