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

Modeling and Model-Based Control Of Multi-Mode Combustion Engines for Closed-Loop SI/HCCI Mode Transitions with Cam Switching Strategies.

Homogeneous charge compression ignition (HCCI) combustion has been investigated by many researchers as a way to improve gasoline engine fuel economy through highly dilute unthrottled operation while maintaining acceptable tailpipe emissions. A major concern for successful implementation of HCCI is that it's feasible operating region is limited to a subset of the full engine regime, which necessitates mode transitions between HCCI and traditional spark ignition (SI) combustion when the HCCI region is entered/exited. The goal of this dissertation is to develop a methodology for control-oriented modeling and model-based feedback control during such SI/HCCI mode transitions. The model-based feedback control approach is sought as an alternative to those in the SI/HCCI transition literature, which predominantly employ open-loop experimentally derived actuator sequences for generation of control input trajectories. A model-based feedback approach has advantages both for calibration simplicity and controller generality, in that open-loop sequences do not have to be tuned, and that use of nonlinear model-based calculations and online measurements allows the controller to inherently generalize across multiple operating points and compensate for case-by-case disturbances. In the dissertation, a low-order mean value modeling approach for multi-mode SI/HCCI combustion that is tractable for control design is described, and controllers for both the SI to HCCI (SI-HCCI) and HCCI to SI (HCCI-SI) transition are developed based on the modeling approach. The model is shown to fit a wide range of steady-state actuator sweep data containing conditions pertinent to SI/HCCI mode transitions, and is extended to capture transient SI-HCCI transition data through using an augmented residual gas temperature parameter. The mode transition controllers are experimentally shown to carry out SI-HCCI and HCCI-SI transitions in several operating conditions with minimal tuning, though the validation in the SI-HCCI direction is more extensive. The model-based control architecture is also equipped with an online parameter updating routine, to attenuate error in model-based calculations and improve robustness to engine aging and cylinder to cylinder variability. Experimental examples at multiple operating conditions illustrate the ability of the parameter update routine to improve controller performance by using transient data to tune the model parameters for enhanced accuracy during SI-HCCI mode transitions.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113351/1/pgoz_1.pd

Modeling and Control of Maximum Pressure Rise Rate in RCCI Engines

Low Temperature Combustion (LTC) is a combustion strategy that burns fuel at lower temperatures and leaner mixtures in order to achieve high efficiency and near zero NOx emissions. Since the combustion happens at lower temperatures it inhibits the formation of NOx and soot emissions. One such strategy is Reactivity Controlled Compression Ignition (RCCI). One characteristic of RCCI combustion and LTC com- bustion in general is short burn durations which leads to high Pressure Rise Rates (PRR). This limits the operation of these engines to lower loads as at high loads, the Maximum Pressure Rise Rate (MPRR) hinders the use of this combustion strategy. This thesis focuses on the development of a model based controller that can control the Crank Angle for 50% mass fraction burn (CA50) and Indicated Mean Effective Pressure (IMEP) of an RCCI engine while limiting the MPRR to a pre determined limit. A Control Oriented Model (COM) is developed to predict the MPRR in an RCCI engine. This COM is then validated against experimental data. A statistical analysis of the experimental data is conducted to understand the accuracy of the COM. The results show that the COM is able to predict the MPRR with reasonable accuracy in steady state and transient conditions. Also, the COM is able to capture the trends during transient operation. This COM is then included in an existing cycle by cycle dynamic RCCI engine model and used to develop a Linear Parameter Varying (LPV) representation of an RCCI engine using Data Driven Modeling (DDM) approach with Support Vector Machines (SVM). This LPV representation is then used along with a Model Predictive Controller (MPC) to control the CA50 and IMEP of the RCCI engine model while limiting the MPRR. The controller was able to track the desired CA50 and IMEP with a mean error of 0.9 CAD and 4.7 KPa respectively while maintaining the MPRR below 5.8 bar/CAD

Machine Learning for Identification and Optimal Control of Advanced Automotive Engines.

The complexity of automotive engines continues to increase to meet increasing performance requirements such as high fuel economy and low emissions. The increased sensing capabilities associated with such systems generate a large volume of informative data. With advancements in computing technologies, predictive models of complex dynamic systems useful for diagnostics and controls can be developed using data based learning. Such models have a short development time and can serve as alternatives to traditional physics based modeling. In this thesis, the modeling and control problem of an advanced automotive engine, the homogeneous charge compression ignition (HCCI) engine, is addressed using data based learning techniques. Several frameworks including design of experiments for data generation, identification of HCCI combustion variables, modeling the HCCI operating envelope and model predictive control have been developed and analyzed. In addition, stable online learning algorithms for a general class of nonlinear systems have been developed using extreme learning machine (ELM) model structure.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/102392/1/vijai_1.pd

Measured and Modeled Performance of a Spring Dominant Free Piston Engine Generator

Free Piston Engine Generators (FPEG) directly convert the reciprocating piston motion into electricity by using a linear alternator. Unlike conventional engines with piston motion restricted by a crankshaft mechanism, the FPEG piston motion is constrained by the energy available in the system. When stiff springs are considered in the design, the FPEG system attains high frequency with high power and efficiency. The main objective of this research was to model stiff spring-assisted FPEG system dynamics and performance accurately, and to apply the modeling results to the development of a 1kW, spark ignited, natural gas fueled, FPEG experimental prototype. The experimental data was further utilized to refine and improve the existing model. First, a MATLAB®/Simulink based multi-cycle numerical model was developed for single and dual cylinder FPEG systems to study the effects of major design parameters on FPEG dynamics and performance. When stiff springs were added, the dynamics became more sinusoidal and symmetric with respect to the initial starting position. For a total displacement of 34 cc, trapped compression ratio of 8.25, and assumed combustion efficiency of 95%, the modeled frequency and electric power varied from 72.3 Hz to 80.8 Hz and 0.81 kW to 0.88 kW for a single cylinder FPEG as the spring stiffness changed from 372 kN/m to 744 kN/m. For a dual cylinder FPEG with the same conditions, these modeled values changed from 76.8 Hz to 84.1 Hz and 1.7 kW to 1.8 kW with increasing spring stiffness. The numerical model was then expanded for sensitivity studies of major design parameters. When FPEG operating conditions were considered, the effective stroke length was found to have a dominant effect on efficiency followed by compression ratio, cylinder bore, and spring stiffness respectively. The experimental FPEG prototype generating 550 W of electricity with indicated efficiencies exceeding 13.8% was used for model validation. Finally, the stable FPEG system requires a control strategy to match the power generated by the engine to the power demanded by the alternator. A model-based control strategy was developed in Stateflow® for alternator mode switching, calibration maps, energy management, ignition and fuel injection timings. With the proposed control strategy and stiff spring dominance, the modeled and experimental FPEG system maintained stable operation with cycle-to-cycle variations less than 5%