Robust sliding mode‐based extremum‐seeking controller for reaction systems via uncertainty estimation approach

"This paper deals with the design of a robust sliding mode‐based extremum‐seeking controller aimed at the online optimization of a class of uncertain reaction systems. The design methodology is based on an input–output linearizing method with variable‐structure feedback, such that the closed‐loop system converges to a neighborhood of the optimal set point with sliding mode motion. In contrast with previous extremum‐seeking control algorithms, the control scheme includes a dynamic modelling‐error estimator to compensate for unknown terms related with model uncertainties and unmeasured disturbances. The proposed online optimization scheme does not make use of a dither signal or a gradient‐based optimization algorithm. Practical stabilizability for the closed‐loop system around to the unknown optimal set point is analyzed. Numerical experiments for two nonlinear processes illustrate the effectiveness of the proposed robust control scheme.

Lyapunov based optimal control of a class of nonlinear systems

Optimal control of nonlinear systems is in fact difficult since it requires the solution to the Hamilton-Jacobi-Bellman (HJB) equation which has no closed-form solution. In contrast to offline and/or online iterative schemes for optimal control, this dissertation in the form of five papers focuses on the design of iteration free, online optimal adaptive controllers for nonlinear discrete and continuous-time systems whose dynamics are completely or partially unknown even when the states not measurable. Thus, in Paper I, motivated by homogeneous charge compression ignition (HCCI) engine dynamics, a neural network-based infinite horizon robust optimal controller is introduced for uncertain nonaffine nonlinear discrete-time systems. First, the nonaffine system is transformed into an affine-like representation while the resulting higher order terms are mitigated by using a robust term. The optimal adaptive controller for the affinelike system solves HJB equation and identifies the system dynamics provided a target set point is given. Since it is difficult to define the set point a priori in Paper II, an extremum seeking control loop is designed while maximizing an uncertain output function. On the other hand, Paper III focuses on the infinite horizon online optimal tracking control of known nonlinear continuous-time systems in strict feedback form by using state and output feedback by relaxing the initial admissible controller requirement. Paper IV applies the optimal controller from Paper III to an underactuated helicopter attitude and position tracking problem. In Paper V, the optimal control of nonlinear continuous-time systems in strict feedback form from Paper III is revisited by using state and output feedback when the internal dynamics are unknown. Closed-loop stability is demonstrated for all the controller designs developed in this dissertation by using Lyapunov analysis --Abstract, page iv

Dither-less extremum seeking for hydrogen minimization in PEM fuel cells

This paper presents a nonsmooth adaptive extremum seeker that minimizes the hydrogen consumption in a fuel-cell system. The extremum seeker operates by estimating the gradient of the objective function but, unlike other seekers, it does not require a dither signal to produce such estimate. The absence of a dither signal simplifies the choice of parameter values for the seeker, and more importantly, it allows it to converge to the optimal value exactly, not only to a small neighborhood. The proper functioning of the proposed scheme is proved using nonsmooth Lyapunov analysis. The strategy is tested on the input-output map of a real polymer electrolyte fuel cell.The research of C. Kunusch has been supported by the Seventh Framework Programme of the European Community through the Marie Curie actions (GA: PCIG09-GA-2011-293876), the Puma-Mind project (GA: FCH-JU-2011-1-303419), the CICYT project DPI2011-25649 (MINECO-Spain), the CSIC MACPERCON project (201250E027) and the CSIC JAE-DOC Research Programme.Peer Reviewe

Investigation of Some Self-Optimizing Control Problems for Net-Zero Energy Buildings

Green buildings are sustainable buildings designed to be environmentally responsible and resource efficient. The Net-Zero Energy Building (NZEB) concept is anchored on two pillars: reducing the energy consumption and enhancing the local energy generation. In other words, efficient operation of the existing building equipment and efficient power generation of building integrated renewable energy sources are two important factors of NZEB development. The heating, ventilation and air conditioning (HVAC) systems are an important class of building equipment that is responsible for large portion of building energy usage, while the building integrated photovoltaic (BIPV) system is well received as the key technology for local generation of clean power. Building system operation is a low-investment practice that aims low operation and maintenance cost. However, building HVAC and BIPV are systems subject to complicated intrinsic processes and highly variable environmental conditions and occupant behavior. Control, optimization and monitoring of such systems desire simple and effective approaches that require the least amount of model information and the use of smallest number but most robust sensor measurements. Self-optimizing control strategies promise a competitive platform for control, optimization and control integrated monitoring for building systems, and especially for the development of cost-effective NZEB. This dissertation study endorses this statement with three aspects of work relevant to building HVAC and BIPV, which could contribute several small steps towards the ramification of the self-optimizing control paradigm. This dissertation study applies self-optimizing control techniques to improve the energy efficiency of NZEB from two aspects. First, regarding the building HVAC efficiency, the dither based extremum seeking control (DESC) scheme is proposed for energy efficient operation of the chilled-water system typically used in the commercial building ventilation and air conditioning (VAC) systems. To evaluate the effectiveness of the proposed control strategy, Modelica based dynamic simulation model of chilled water chiller-tower plant is developed, which consists of a screw chiller and a mechanical-draft counter-flow wet cooling tower. The steady-state performance of the cooling tower model is validated with the experimental data in a classic paper and good agreement is observed. The DESC scheme takes the total power consumption of the chiller compressor and the tower fan as feedback, and uses the fan speed setting as the control input. The inner loop controllers for the chiller operation include two proportional-integral (PI) control loops for regulating the evaporator superheat and the chilled water temperature. Simulation was conducted on the whole dynamic simulation model with different environment conditions. The simulation results demonstrated the effectiveness of the proposed ESC strategy under abrupt changes of ambient conditions and load changes. The potential for energy savings of these cases are also evaluated. The back-calculation based anti-windup ESC is also simulated for handling the integral windup problem due to actuator saturation. Second, both maximum power point tracking (MPPT) and control integrated diagnostics are investigated for BIPV with two different extremum seeking control strategies, which both would contribute to the reduction of the cost of energy (COE). In particular, the Adaptive Extremum Seeking Control (AESC) is applied for PV MPPT, which is based on a PV model with known model structure but unknown nonlinear characteristics for the current-voltage relation. The nonlinear uncertainty is approximated by a radial basis function neural network (RBFNN). A Lyapunov based inverse optimal design technique is applied to achieve parameter estimation and gradient based extremum seeking. Simulation study is performed for scenarios of temperature change, irradiance change and combined change of temperature and irradiance. Successful results are observed for all cases. Furthermore, the AESC simulation is compared to the DESC simulation, and AESC demonstrates much faster transient responses under various scenarios of ambient changes. Many of the PV degradation mechanisms are reflected as the change of the internal resistance. A scheme of detecting the change of PV internal shunt resistance is proposed using the available signals in the DESC based MPPT with square-wave dither. The impact of the internal resistance on the transient characteristics of step responses is justified by using the small-signal transfer function analysis. Simulation study is performed for both the single-string and multi-string PV examples, and both cases have demonstrated successful results. Monotonic relationship between integral error indices and the shunt internal resistance is clearly observed. In particular, for the multi-string, the inter-channel coupling is weak, which indicates consistent monitoring for multi-string operation. The proposed scheme provides the online monitoring ability of the internal resistance condition without any additional sensor, which benefits further development of PV degradation detection techniques

Extremum Seeking Control of Hybrid Ground Source Heat Pump System

The ground source heat pump (GSHP) technology is a renewable alternative for space conditioning by rejecting/absorbing heat to/from the ground, which has demonstrated higher energy efficiency for residential and commercial buildings. As the system capacity is limited by the initial cost of construction of ground-loop heat exchanger (GHE), developing the so-called Hybrid GSHP system by utilizing supplemental heat rejecters such as cooling towers has emerged as a cost-effective alternative. In practice, operational efficiency of Hybrid GSHP system mainly depends on 1) the actual characteristics of heat pump, cooling tower, GHE and other equipment; 2) ambient air and ground conditions. In particular, the GHE heat transfer is heavily affected by the ground thermal characteristics which, however, is difficult and expensive in practice to determine due to the complexity of soil type and distribution. In addition, the actual cooling tower characteristics can vary significantly. Such uncertainties bring forth dramatic difficulty for successful application of model based control or optimization methods. In this study, an extremum seeking control (ESC) strategy is proposed for efficient operation of a hybrid GSHP system with cooling tower, which minimizes the total power (i.e. GHE loop water pump, cooling tower fan and pump, and the heat-pump compressor) consumption by tuning the air-flow rate of the cooling tower fan and the GHE loop water flow rate. To evaluate the proposed control method, a Modelica based model of the Hybrid GSHP system is developed by utilizing the Buildings Library developed by the Lawrence Berkeley National Laboratory, which consists of a 20-borehole GHE, a water-to-water heat pump, a counter-flow cooling tower and a plate heat exchanger. The transient conduction model of vertical GHE in the Buildings Library is adopted, which is based on a finite-volume method inside the borehole and cylindrical source model outside the borehole. A variable-flow water pump model is constructed for the GHE water loop, which gives power consumption under different operating scenarios. A cooling tower model in the Buildings Library is adopted, which is a static polynomial model based on a York cooling tower correlation. The relative air flow rate can be regulated to maintain the leaving water temperature at the setpoint, and then the corresponding fan power consumption is obtained. The heat pump model is based on the evaporator temperature, condenser temperature and Carnot efficiency. An inner-loop proportional-integral (PI) controller is implemented to regulate the evaporator leaving water temperature at 7 deg-C. Under the air wet-bulb temperature of 35 deg-C and dry-bulb temperature 23 deg-C, steady-state simulation of the plant model yields the static map of the total power with respect to the cooling tower relative air flow rate and the GHE water flow rate, which indicates about 25% power variation across the adjustable range of inputs. Simulation was conducted in two conditions: change in evaporator inlet water temperature and change in ambient air condition. The simulation study under way is to validate the effectiveness of the proposed ESC strategy, and the potential for energy saving will also be evaluated

Energy efficient control of electrostatically actuated MEMS

Plenty of Micro-electro-mechanical Systems (MEMS) devices are actuated using electrostatic forces, and specially, parallel-plate actuators are extensively used, due to the simplicity of their design. Nevertheless, parallel-plate actuators have some limitations due to the nonlinearity of the generated force. The dissertation analyzes the dynamics of the lumped electrostatically actuated nonlinear system, in order to obtain insight on its characteristics, define desired performance goals and implement a controller for energy efficient robustly stable actuation of MEMS resonators. In the first part of the dissertation, the modeling of the electromechanical lumped system is developed. From a complete distributed parameters model for MEMS devices which rely on electrostatic actuation, a concentrated parameters simplification is derived to be used for analysis and control design. Based on the model, energy analysis of the pull-in instability is performed. The classic approach is revisited to extend the results to models with a nonlinear springs. Analysis of the effect of dynamics is studied as an important factor for the stability of the system. From this study, the Resonant Pull-in Condition for parallel-plate electrostatically actuated MEMS resonators is defined and experimentally validated. Given the importance of the nonlinear dynamics and its richness in behaviors, Harmonic Balance is chosen as a tool to characterize the steady-state oscillation of the resonators. This characterization leads to the understanding of the key factors for large and stable oscillation of resonators. An important conclusion is reached, Harmonic Balance predicts that any oscillation amplitude is possible for any desired frequency if the appropriate voltage is applied to the resonator. And the energy consumption is dependent on this chosen oscillation frequency. Based on Harmonic Balance results, four main goals are defined for the control strategy: Stable oscillation with large amplitudes of motion; Robust oscillation independently of MEMS imperfections; Pure sinus-like oscillation for high-grade sensing; and Low energy consumption. The second part of the dissertation deals with the controller selection, design and verification. A survey of prior work on MEMS control confirms that existing control approaches cannot provide the desired performance. Consequently, a new three-stage controller is proposed to obtain the desired oscillation with the expected stability and energy efficiency. The controller has three different control loops. The first control loop includes a Robust controller designed using on µ-synthesis, to deal with MEMS resonators uncertainties. The second control loop includes an Internal-Model-Principle Resonant controller, to generate the desired control action to obtain the desired oscillation. And the third control loop handles the energy consumption minimization through an Extremum Seeking Controller, which selects the most efficient working frequency for the desired oscillation. The proposed controller is able to automatically generate the needed control voltage, as predicted by the Harmonic Balance analysis, to operate the parallel-plate electrostatically actuated MEMS resonator at the desired oscillation. Performance verification of stability, robustness, sinus-like oscillation and energy efficiency is carried out through simulation. Finally, the needed steps for a real implementation are analyzed. Independent two-sided actuation for full-range amplitude oscillation is introduced to overcome the limitations of one-sided actuation. And a modification of standard Electromechanical Amplitude Modulation is analyzed and validated for position feedback implementation. With these improvements, a MEMS resonator with the desired specifications for testing the proposed control is designed for fabrication. Based on this design, testing procedure is discussed as future work.Molts microsistemes (MEMS) són actuats amb forces electrostàtiques, i especialment, els actuadors electrostàtics de plaques paral.leles són molt usats, degut a la simplicitat del seu disseny. Tot i això, aquests actuadors tenen limitacions degut a la no-linealitat de les forces generades. La tesi analitza el sistema mecànic no-lineal actuat electrostàticament que forma el MEMS, per tal d'entendre'n les característiques, definir objectius de control de l'oscil.lació, i implementar un controlador robust, estable i eficient energèticament. A la primera part de la tesi es desenvolupa el modelat del sistema electromecànic complert. A partir de la formulació de paràmetres distribuïts aplicada a dispositius MEMS amb actuació electrostàtica, es deriva una formulació de paràmetres concentrats per a l'anàlisi i el disseny del control. Basat en aquest model, s'analitza energèticament la inestabilitat anomenada Pull-in, ampliant els resultats de l'enfocament clàssic al model amb motlles no-lineals. Dins de l'anàlisi, l'evolució dinàmica s'estudia per ser un factor important per a l'estabilitat. D'aquest estudi, la Resonant Pull-in Condition per a actuadors electrostàtics de plaques paral.leles es defineix i es valida experimentalment. Donada la importància de la dinàmica no-lineal del sistema i la seva riquesa de comportaments, s'utilitza Balanç d'Harmònics per tal de caracteritzar les oscil.lacions en estacionari. Aquesta caracterització permet entendre els factors claus per a obtenir oscil.lacions estables i d'amplitud elevada. El Balanç d'Harmònics dóna una conclusió important: qualsevol amplitud d'oscil.lació és possible per a qualsevol freqüència desitjada si s'aplica el voltatge adequat al ressonador. I el consum energètic associat a aquesta oscil.lació depèn de la freqüència triada. Llavors, basat en aquests resultats, quatre objectius es plantegen per a l'estratègia de control: oscil.lació estable amb amplituds elevades; robustesa de l'oscil.lació independentment de les imperfeccions dels MEMS; oscil.lació sinusoïdal sense harmònics per a aplicacions d'alta precisió; i baix consum energètic. La segona part de la tesi tracta la selecció, disseny i verificació dun controlador adequat per a aquests objectius. La revisió dels treballs existents en control de MEMS confirma que cap dels enfocaments actuals permet obtenir els objectius desitjats. En conseqüència, es proposa el disseny d'un nou controlador amb tres etapes per tal d'obtenir l'oscil.lació desitjada amb estabilitat i eficiència energètica. El controlador té tres llaços de control. Al primer llaç, un controlador robust dissenyat amb µ-síntesis gestiona les incertes es dels MEMS. El segon llaç inclou un controlador Ressonant, basat en el Principi del Model Intern, per a generar l'acció de control necessària per a obtenir l'oscil.lació desitjada. I el tercer llaç de control gestiona la minimització de l'energia consumida mitjançant un controlador basat en Extremum Seeking, el qual selecciona la freqüència de treball més eficient energèticament per a l'oscil.lació triada. El controlador proposat és capaç de generar automàticament el voltatge necessari, igual al previst pel Balanç d'Harmònics, per tal d'operar electrostàticament amb plaques paral.leles els ressonadors MEMS. Mitjançant simulació se'n verifica l'estabilitat, robustesa, inexistència d'harmònics i eficiència energètica de l'oscil.lació. Finalment, la implementació real és analitzada. En primer lloc, un nou esquema d'actuació per dos costats amb voltatges independents es proposa per aconseguir l'oscil.lació del ressonador en tot el rang d'amplituds. I en segon lloc, una modificació del sensat amb Modulació d'Amplitud Electromecànica s'utilitza per tancar el llaç de control de posició. Amb aquestes millores, un ressonador MEMS es dissenya per a ser fabricat i validar el control. Basat en aquest disseny, es proposa un procediment de test plantejat com a treball futur.Postprint (published version

Extremum-Seeking Guidance and Conic-Sector-Based Control of Aerospace Systems

This dissertation studies guidance and control of aerospace systems. Guidance algorithms are used to determine desired trajectories of systems, and in particular, this dissertation examines constrained extremum-seeking guidance. This type of guidance is part of a class of algorithms that drives a system to the maximum or minimum of a performance function, where the exact relation between the function's input and output is unknown. This dissertation abstracts the problem of extremum-seeking to constrained matrix manifolds. Working with a constrained matrix manifold necessitates mathematics other than the familiar tools of linear systems. The performance function is optimized on the manifold by estimating a gradient using a Kalman filter, which can be modified to accommodate a wide variety of constraints and can filter measurement noise. A gradient-based optimization technique is then used to determine the extremum of the performance function. The developed algorithms are applied to aircraft and spacecraft. Control algorithms determine which system inputs are required to drive the systems outputs to follow the trajectory given by guidance. Aerospace systems are typically nonlinear, which makes control more challenging. One approach to control nonlinear systems is linear parameter varying (LPV) control, where well-established linear control techniques are extended to nonlinear systems. Although LPV control techniques work quite well, they require an LPV model of a system. This model is often an approximation of the real nonlinear system to be controlled, and any stability and performance guarantees that are derived using the system approximation are usually void on the real system. A solution to this problem can be found using the Passivity Theorem and the Conic Sector Theorem, two input-output stability theories, to synthesize LPV controllers. These controllers guarantee closed-loop stability even in the presence of system approximation. Several control techniques are derived and implemented in simulation and experimentation, where it is shown that these new controllers are robust to plant uncertainty.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143993/1/aexwalsh_1.pd

Adaptive Systems: History, Techniques, Problems, and Perspectives

We survey some of the rich history of control over the past century with a focus on the major milestones in adaptive systems. We review classic methods and examples in adaptive linear systems for both control and observation/identification. The focus is on linear plants to facilitate understanding, but we also provide the tools necessary for many classes of nonlinear systems. We discuss practical issues encountered in making these systems stable and robust with respect to additive and multiplicative uncertainties. We discuss various perspectives on adaptive systems and their role in various fields. Finally, we present some of the ongoing research and expose problems in the field of adaptive control