Dynamic Systems Control Laboratory
Selected Research Projects
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.
Significant advances in matrix methods of structural analysis and an increased digital computing capability has resulted in the emergence of automated structural synthesis as a viable design tool. In this work, the configuration and sizing design of structures accounting for the likelihood of structural component failure is addressed. The approach taken utilizes Genetic Algorithms, a nontraditional optimization technique which evolves" structures based on Darwin's survival of the fittest" theories such that they are robust to component failure.Currently, computer studies are being performed in the areas of Genetic Algorithm development. Future testing in the Laboratory will involve the construction and testing of truss structures with dynamically failing members.
Fundamental to the problem of control component placement (sensors and actuators) are: (i) the definition of an appropriate criterion representing the desirability of configurations, (ii) the development of a computationally efficient method for the evaluation of this criterion, and (iii) the development of algorithms to cycle through possible candidate configurations. Criterion reflecting the probability of component failure are currently under development using the framework of controllability and observability grammians. The performance of Genetic Algorithms in solving the resulting large order combinatorial problem is currently being investigated.
Experimental studies are aimed at validating the proposed criterion and testing control performance.
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.
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
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.
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.
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.
Fault-tolerant control law design is required for the successful operation of FTISS. It can easily be shown that in a FTISS with 400 components, each with an exponential distribution of time to failure with a mean time to failure of 100,000 hours (~12.6 years), once can expect a component failure every 10 days. By fault-tolerant control, we mean that after a component failure, the remaining FTISS maintains stability, although the performance of the FTISS system will obviously be degraded. To improve performance, the fault must first be detected and isolated. With knowledge of which component has failed, a new control system can be reconfigured on-line to enhance performance.
Fuzzy controllers can be viewed in the general stream of heuristic based expert control systems, characterized additionally by a suitable mechanism for representing vague human judgments. In this research, the Fuzzy Control heuristics embody the desire of maintaining stability at all times in light of failure.Experimental work is focussed on real-time implementation issues related to fuzzy control and various performance studies.
Failure Detection & Isolation of Structural Components: Minimum Rank Perturbation Theory & Eigenstructure Assignment
The determination of location and extent of structural damage is of significant importance in many engineering systems ranging from the nations infrastructure (bridges) to future large space structures such as the Space Station. The problem to be solved is to determine the location and extent of structural damage from measured dynamic properties.
The approaches currently under study have their basis in linear system analysis and control theory. Theoretical and experimental studies on small and large scale structures is underway. The work is consistent with the development of finite element model refinement technology.
The detection & isolation of failed sensors and actuators is required for eventual system reconfiguration. Two approaches are currently under investigation. The first approach is based upon system realization theory. This theory makes use of the Eigensystem Realization Algorithm (ERA) developed at NASA LaRC and uses realization redundancy as opposed to the more traditional hardware and/or model redundancy. The second approach exploits the pattern recognition capability of Neural Networks to recognize the failed control component.
Current studies involve both computer simulation and experimental studies. Future experimental research is aimed at real-time implementation issues.
Reconfiguration is the process in which the information concerning the most recent failure is utilized to optimize the use of the remaining structure / control components. Genetic Algorithm Learning Control and Neural Network feature recognition capabilities are being investigated for use as reconfiguration engines.
Experimental studies involving real-time Genetic Algorithm Learning Control and the implementation of advanced control laws by Neural Networks are underway.
Future intelligent structural systems will need to satisfy stringent performance requirements on multiple system outputs despite both disturbances and modeling errors and uncertainties. To this end, the solution of Multiobjective robust control design problems is essential for FTISS. It can be shown that the above control problems can be mathematically formulated as feasibility problems which require to find a matrix in the intersection of a family of constraint sets.
Numerical methods that utilize the orthogonal projections onto the constraint sets provide effective ways to solve the robust Multiobjective control problems. Currently, improved numerical algorithms are developed, that make use of the simple geometry of the constraint sets to achieve faster convergence rates. In addition, the possibility of parallel implementation of these algorithms is examined.
This research investigates the use of matrix inequality control methods and alternating projection algorithms to solve mullet objective control design problems for mechanical and structural systems. The project focuses on systematic methods to design low-order decentralized controllers in the presence os system uncertainties, unwanted disturbances and saturation constraints. The vector second-order finite element representation of the structural systems exploited to provide simplified and optimized control schemes. The use of matrix inequality and projection methods for optimal model reduction and reduced-order filtering is also investigated. Funding for this project is provided by the UH Institute of Space Systems Operations and NSF.
Novel matrix inequality and alternating projection algorithms are investigated to detect damage in structural systems based on measured eigen frequencies and eigen vectors. The damage detection problem is formulated as an optimization problem of computing the stiffness matrix of the damaged structure that is consistent with the measured parameters, the connectivity of the system and the localized nature of damage.