Selected Publications (Full  text - pdf)

 Curriculum Vitae (Printable  Version - pdf)  

 Aerospace Engineering  Graduate Program

 Engine Control Research  Laboratory

 Dynamic Systems Control  Laboratory

Dept. of Mech. Engineering

N207 Engineering Building 1

University of Houston

Houston, TX 77204-4006

Tel : 713-743-4387

Fax: 713-743-4503

Email: karolos@uh.edu

SELECTED RESEARCH PROJECTS

Integrated Plant/Control Design Methods

           Optimized design of complex controlled systems requires the simultaneous calculation of plant parameters (such as geometric characteristics, system configuration, selection of materials and material properties) and feedback control parameters (such as feedback control gains, controller complexity, and sensor/actuator number and location) to compensate for the strong coupling between the plant dynamics and the controller implementation. This research goes beyond the traditional two-step sequential plant design followed by control design to achieve an integrated design of the plant and the controller reaching optimized closed-loop performance and robustness to disturbances, plant variability and uncertainty. We have developed novel iterative redesign methods along with efficient convex computational algorithms that provide guaranteed convergence to optimize designs that minimize total system mass, active control effort, and system sensitivity to disturbances and varying parameters. Our methods have shown that for a large class of systems (linear systems with affine representation of system parameters and control gains) global optimality can be achieved with the proposed methods in a very efficient convex optimization computational setting. This research is particularly important for complex large scale systems, such as large space structures and smart structures with a large number of sensors and actuators.

Design of Low-order Dynamic Controllers

          The problem of designing low-order dynamic feedback controllers with guaranteed stability, robustness and optimized performance for large-scale systems is a long-standing open problem in feedback control systems. Such controllers have increased reliability, minimal complexity and lower implementation cost. We have provided a novel formulation of the low-order control design problem in terms of linear matrix inequalities (LMIs) coupled with matrix rank constraints, and we have developed novel computational algorithms based on alternating projection techniques combined with interior point optimization algorithms to address this problem. The proposed computational schemes exploit the geometric structure of the problem to obtain controllers with predetermined dynamic order and performance bounds. The vector-second-order finite element representation of structural systems has been exploited to provide simplified and optimized control schemes. The techniques have been extended to address a large class of practical closed-loop performance and robustness objectives for nominal, uncertain and parameter dependent systems. Also, large-scale system model order reduction and low-order filtering and estimation problems have been solved using the developed analytical and computational tools. Controller decentralization constraints to allow distributed control have been addressed in a similar setting.

Control of Systems with Variable Time Delays and Variable Sampling Rates

            Time-delays in a control system feedback loop could limit the achievable level of performance and lead to closed-loop. We have developed systematic methods to analyze the stability, disturbance rejection and robustness properties of linear, parameter dependent and nonlinear systems that are subject to multiple variable time-delays in the input and state variables. The results have been extended to control synthesis via parameter dependent controllers that adapt their dynamics to the delay variability. Our methods utilize appropriate delay-dependent Lyapunov functionals, and the corresponding delayed system analysis and synthesis conditions are formulated in terms of parameter dependent linear matrix inequalities (LMIs) that are solved based on appropriate discretization of the parameter space. Extensive numerical computations and simulations have demonstrated the capability of the new control schemes to compensate for the variable delays.
            The control problem subject to variable sampling rates has been addressed using similar parameter dependent robust gain scheduled methodologies. A lifting approach has been developed to convert a sampled-data system to a discrete-time system where the corresponding discrete-time signals take their values in a function space such that system stability and system norms are preserved through lifting. An important fact is that although finite-dimensional systems are lifted to systems with infinite dimensional input and output spaces, the state dimension of the lifted system is finite and equal to the dimension of the original system. Hence, finite-dimensional discrete-time parameter-dependent robust control theory can be applied. We are also interested in gain-scheduling problems where the sampling interval is a function of the parameter vector. A matrix inequality formulation of the lifted parameter-varying discrete-time system has been developed.

Control of Systems with Saturation

            A robust gain-scheduled approach has been developed to design controllers for parameter-varying systems with actuator saturation constraints. This is accomplished by representing the status of each saturated or non-saturated actuator as a varying parameter measurable in real-time, and the parameter-varying controller is then gain-scheduled based on these parameters. Hence, the controller is adapted in real-time to the saturation levels. Therefore, the control of a nonlinear system with input saturation constraints is accomplished in a generalized gain-scheduled framework where scheduling on different operating conditions is used to accommodate the nonlinear system behavior, and scheduling on the actuation is used to accommodate the saturation constraints. Appropriate weighting functions that depend on the saturation levels can provide shifting of the control focus from stability in the presence of saturation to performance in the case where the actuators operate in their linear region. In addition, the control of systems with actuator saturation position and rate constraints has been examined following a gain-scheduling formulation. The results have been validated in detailed engine control and aircraft control simulation studies.

Control of Systems with Hysteresis

            Many electro-mechanical and structural systems exhibit hysteretic behavior due to friction, phase transition or backlash, such as, smart materials (shape memory alloys (SMAs), piezoceramic and magnetostrictive materials), concrete reinforced structures, gear systems and vibrating systems with umbilicals. Uncompensated hysteresis causes a number of undesirable effects, including poor performance, steady-state errors, limit cycle behavior and loss of stability. In high performance systems, such as, microgravity isolation systems, machining of precision parts, and lithography of microelectronic devices, hysteretic effects can result in severe degradation of quality and performance. In this ongoing project we seek to provide systematic feedback control laws implemented in the control computer that regulates the hysteretic system to optimally adapt the hysteresis model based on the current operating condition. Our work focuses on adaptive control laws that are self-scheduled based on the magnitude of the input signal, the excitation frequency and the variability of the hysteretic loop as a function of time. We utilize adaptive on-line identification of the parameters of Preisach-type hysteretic models and parameter dependent controllers that vary dynamically based on the operating environment and the current hysteretic model. The corresponding control synthesis problem is formulated as an infinite dimensional convex optimization problem that can be solved with appropriate discretization to obtain the control gain coefficients in a parametric form as a function of the current operating point.

Robust Gain-Scheduled Control of Internal Combustion Engines

            This project involves the design of robust multivariable controllers for internal combustion engines to improve their performance, reliability, and fuel economy, and to minimize exhaust emissions by regulating the engine speed and the air-fuel ratio. The proposed research has resulted in novel operating-condition-dependent controllers that take into account the engine model uncertainties and nonlinearities, the variable time-delays and the torque load disturbances. Novel matrix inequality algorithms are utilized to obtain parameter-dependent Lyapunov functions that guarantee stability, regulation, and robustness for all engine operating conditions. Recent work has also addressed the Selective Catalytic Reduction (SCR) engine after-treatment control problem for minimizing emissions. The control objective is to provide optimal regulation of engine parameters (fueling, engine timing, engine air flow, variable geometry turbocharger position and speed, exhaust gas recirculation valve opening) and SCR catalytic reduction parameters (urea injection timing and amount) for maximum reliability and performance achieved with the lowest possible emissions and fuel consumption. We have developed diesel engine and SCR controllers that are self-scheduled (adapted) in real-time based on the current operating conditions, control-loop delays and fuel/urea saturation levels for optimized performance, economy and reliability. Parameter varying control methodologies developed by our group have been utilized to address the above multivariable optimal control problem effectively. The corresponding control synthesis problem is reduced to solving a set of Linear Matrix Inequalities (LMIs). LMI optimization is reliable and efficient convex optimization with available powerful computational algorithms for solution. Detailed nonlinear diesel engine simulation and catalytic reduction models, identification-based models and data have been provided by automotive companies and the controllers have been validated in hardware-in-the-loop tests.

Microgravity Isolation for Space Station Experiments

            A critical function of the International Space Station (ISS) is to serve as a premier on-orbit microgravity laboratory for conducting acceleration-sensitive scientific research experiments on active rack isolation platforms. The extremely stringent micro-g vibration isolation requirement, the presence of variable umbilical stiffness nonlinearities and hysteresis along with inertia coupling of the vibrating system, unmodeled system dynamics and hardware implementation constraints on the controller make this an extremely challenging modeling and control design problem from both a theoretical and a practical perspective. We have applied adaptive feedback control schemes to provide the required experiment vibration isolation and to compensate for the hysteretic stiffeness variability. Hence, the control gains are variable and are adapted on-line to the current operating point in the hysteresis loop. System model uncertainty has been treated in a robust control framework by providing guaranteed closed-loop performance for the vibrating system for all perturbed models that result from the unmodelled dynamics. The computational control synthesis problem for such parameter dependent systems results in a convex optimization problem with Linear Matrix Inequality (LMI) constraints that can be solved efficiently allowing rapid redesign. Projection methodologies on the controller parameter space have been applied to enforce decentralization and fixed architecture control constraints. This project is conducted in collaboration with Boeing Space Systems in Houston.

 Loughborough University -  Visiting Professorship

 IASTED Intelligent Control  Systems Conference 2008 -  Conference Chair