Katie A. Evans

Reduced order controllers for distributed parameter systems: LQG balanced truncation and an adaptive approach

In this paper, two methods are reviewed and compared for designing reduced order controllers for distributed parameter systems. The first involves a reduction method known as LQG balanced truncation followed by MinMax control design and relies on the theory and properties of the distributed parameter system. The second is a neural network based adaptive output feedback synthesis approach, designed for the large scale discretized system and depends upon the relative degree of the regulated outputs. Both methods are applied to a problem concerning control of vibrations in a nonlinear structure with a bounded disturbance.

Reduced-order compensators via balancing and central control design for a structural control problem

Real-time control of a physical system necessitates controllers that are low order. In this article, we compare two balanced truncation methods as a means of designing low-order controllers for a nonlinear cable-mass system. The first is the standard technique of balanced truncation. The second, linear quadratic Gaussian (LQG) balanced truncation, can be thought of as balancing based on the controller, and states that are important from the perspective of control and filter design are retained. The control design applied to each reduced-order model is the central controller. We provide an overview of the central controller and devote attention to the design of this controller in the presence of balancing. Also described in this article is a method for reducing computational time in solving algebraic Riccati equations for the design of low-order LQG balanced controllers.

Target tracking strategies for a nonlinear, flexible aircraft-inspired model

Aeroelastic wing micro aerial vehicle (MAV) concepts are being explored for military and civilian applications. However, on the whole, the issues of control of MAVs are largely unexplored. The authors seek to employ distributed parameter modeling and control theory in an effort to achieve agile flight potential of flexible, morphable wing MAV airframes. In this work, two Euler-Bernoulli beams connected to a rigid mass are used to model the heave dynamics of an aeroelastic wing MAV. A nonlinear aerodynamic lift force acts upon this multiple component structure. The focus of this paper is an effort to employ tools from linear distributed parameter control theory to gain insight into feasibly obtained wing shape, as a bridge to examining optimal wing morphing trajectories for achieving agile flight.

Sensitivities & functional gains for a flexible aircraft-inspired model

Aeroelastic wing micro-autonomous aerial systems (MAAS) concepts are being explored for military and civilian applications. However, on the whole, the issues of control of MAAS are largely unexplored. Controllers designed using methods applicable to larger aircraft are unlikely to realize the agile flight potential of flexible wing MAAS airframes. In this paper, the authors use two Euler-Bernoulli beams connected to a rigid mass to model an aeroelastic wing MAAS. They employ Continuous Sensitivity Equation Methods to examine the sensitivity of the controlled state with respect to variation of the H∞ control parameter, with the primary goal being to gain insight into the flexible dynamics of the system in order to exploit the flexibility for control purposes. Further, the authors examine functional gains in order to determine optimal sensor placement while taking advantage of the flexibility of the MAAS model.

Nonlinear controllers for wing morphing trajectories of a heave dynamics model

A multiple component structure consisting of two Euler-Bernoulli beams connected to a rigid mass is used to model the heave dynamics of an aeroelastic wing micro air vehicle that is acted upon by a nonlinear aerodynamic lift force. In this work we consider two different strategies for designing nonlinear controllers that achieve specified wing morphing trajectories, namely (a) linearization followed by linear quadratic tracking and (b) a feedback linearization inner loop with sliding mode outer loop. We seek to analyze the relative performance of the two controllers as we note the advantages and disadvantages of each approach.

Riccati conditioning and sensitivity for a MinMax controlled cable-mass system

In this paper we present a numerical study that investigates the relationship between the parameter q, used in the design of the MinMax controller, and the conditioning of the approximate algebraic Riccati equations, the sensitivity of the eigenvalues of I-¿2P¿ to ¿ as well as the effect of q on the stability radia and the stability margin of the system. In order to guarantee accurate numerical solutions to the approximate Riccati equations, the Riccati equations must remain well-conditioned for the values of ¿ that are considered. This condition number reflects the combined sensitivity of the Riccati equations to the system inputs A, B, R, C and ¿. In addition, we also consider the sensitivity of the eigenvalues of I-¿2P¿ to ¿. We study the possibility of these sensitivities serving as an indication of the largest value of ¿ for which I-¿2P¿ remains positive definite. This sensitivity could also serve as an indication of the accuracy of the computation of I-¿2P¿. Lastly, in order to design efficient low order controllers, it is important to ensure the robustness of the design. Stability radius and stability margin serve as measures of the robustness of the controller. A one-dimensional nonlinear cable mass system is considered to illustrate these ideas and numerical results are presented.

LQR tracking of a delay differential equation model for the study of nanoparticle dosing strategies for cancer therapy

Currently, the most commonly used treatments for cancerous tumors (chemotherapy, radiation, etc.) have almost no method of monitoring the administration of the treatment for adverse effects in real time. Without any real time feedback or control, treatment becomes a “guess and check” method with no way of predicting the effects of the drugs based on the actual bioavailability to the patients body. One particular drug may be effective for one patient, yet provide no benefit to another. Doctors and scientists do no routinely attempt to quantifiably explain this discrepancy. In this work, mathematical modeling and analysis techniques are joined together with experimentation to gain further insight into the challenges of nanoparticle delivery to tumor sites. There exists a commonly accepted model of drug clearance in the pharmacokinetics community, and it is demonstrated here that this model provides an accurate reflection of reality, as observed in experiment for delivery of gold-coated nanorods. This model is then utilized in a state space feedback control framework to regulate the nanoparticle concentration in the bloodstream. An equal time delay is also introduced in both the state and control input for the purpose of studying alternate dosing strategies. This study will aid in the prediction of the effects of the drugs in a patients body, thus leading to better models for drug regimen and administration.

Atmospheric Wind Energy Extraction by a Micro Autonomous Glider

Extracting energy from thermal wind conditions with a small autonomous air vehicle is considered. A non-linear model predictive controller is developed that embeds a standard glider model and tracks roll, pitch, and yaw angles. Given knowledge of the local wind structure, the flight control system increases the potential energy of the aircraft through autonomous soaring. A typical energy extracting trajectory is investigated through simulation.

Sensitivity analysis for control parameter determination for a nonlinear cable-mass system

The MinMax controller results from a differential game approach to solving the H∞ control problem. As such, the MinMax controller involves a design parameter, which gives a measure of robustness for the controller. There exists no explicit formula for determining the design parameter, and the optimal value must be determined experimentally. Instead of choosing the parameter value experimentally and suffering the computational expense, it would be more efficient if the design parameter could be determined by a prescribed formula based on a mathematically rigorous criterion. In this paper, the author employs continuous sensitivity equation methods to examine the sensitivity of the controlled state with respect to variation of the MinMax control parameter, with the goal being to explore the possibility of determining an efficient assignment of the parameter that is mathematically justified. Numerical simulations are performed on a one-dimensional nonlinear cable-mass system, and the results are presented.

Frequency and time domain analysis of an aeroelastic wing multiple component structure

A multiple component structure consisting of two Euler-Bernoulli beams connected to a rigid mass is used to model the heave dynamics of a wing micro air vehicle. In the time domain, the attainment of a C 0-semigroup in the context of sesquilinear forms is demonstrated. In addition, the closed loop system is demonstrated to generate an exponentially stable C 0-semigroup. In the frequency domain, the infinite dimensional transfer function is determined and used to examine several properties of the system. Finally, an optimal control is used to morph the wings to a desired shape, and simulation results are demonstrated.