Daniel E. Davison

Stabilization in the presence of an uncertain arbitrarily large delay

Handling delays in control systems is difficult and is of long-standing interest. It is well known that, given a finite-dimensional linear time-invariant (LTI) plant and a finite-dimensional LTI stabilizing controller, closed-loop stability will be maintained under a small delay in the feedback loop. However, in some situations there is a large delay, perhaps arising from a slow communications link or a large but variable computational delay (e.g., in a system which uses image processing). While there are techniques available to design a controller to handle a known delay, there is no general theory for designing a controller to handle an arbitrarily large uncertain delay. Here we prove constructively that, given a finite-dimensional LTI plant and an upper bound on the admissible time delay, there exists a linear periodic controller which robustly stabilizes the plant.

Multi-agent stabilisation of the psychological dynamics of one-dimensional crowds

This work is part of an investigation aimed at applying the tools of control theory to gain a deeper understanding of the behaviour and attitudes that develop in individuals and in groups of people, with the goal of ultimately controlling the relevant psychological dynamics. The present treatment investigates an approach to stabilise one-dimensional crowds, that is, structures where people are aligned in a queue. The psychological dynamics considered here are based on the notion of suggestibility put forth by Gustave Le Bon. Control action is carried out by certain authoritative figures, termed control agents, who are interspersed throughout the crowd in some predetermined arrangement, subject to one control agent being positioned at one end of the queue. The main result of this paper is the existence of a state-feedback control law for each control agent that, possibly with some communication among control agents, stabilises the crowd. Advantages of employing multiple control agents instead of a single control agent are highlighted, and, throughout, the main stabilisation results are verified using simulations. Finally, the possibility of extending the control strategy to two-dimensional crowds is briefly explored.

Conformal radiotherapy cancer treatment with multileaf collimators: improving performance with real-time feedback

For over a century, physicians have used external X-ray radiation as a treatment option to destroy or impede the growth of cancerous tumours. This treatment delivers a dose of radiation to a tumour with the goal of irradiating cancerous tissue, while sparing surrounding healthy tissue. To accommodate tumour movement during the treatment and errors in aligning the tumour with the radiation beam, the area to be irradiated is typically made larger than the area of the tumour; this practice ensures the cancerous tissue is irradiated, but is detrimental to the surrounding healthy tissue. Recent medical imaging advances have motivated research studying the use of feedback in radiotherapy to track the tumour position in real time. Feedback permits a reduction in the radiation beam size during treatment, possibly reducing damage to healthy tissue adjacent to the tumour. This paper extends previous results and proposes a feedback control system for the latest generation of radiotherapy machines

The Psychological Dynamics of Students in a Classroom: Modeling and Control Strategies Based on Suggestibility Theory

This work is motivated by the observation that students in a classroom sometimes seem to behave not as a group of independent individuals, but instead as a collective body. Interaction among students leads to psychological dynamics within the class, specifically the propagation of attitudes from student to student. These dynamics tend to be unstable. The goal of this paper is to investigate if it is possible to find a mathematical model that captures the crowd dynamics, and if it is then possible to use control systems techniques to stabilize a crowd. Our approach is to use suggestibility theory to derive a discrete-time nonlinear model, then use observer-based output-feedback control and some simple nonlinear control techniques. Snapshots from several simulations are included.

Controller Design for Multivariable Linear Time-Invariant Unknown Systems

This paper deals with the design of multivariable controllers for stable linear time-invariant multi-input multi-output systems, with an unknown mathematical model, subject to constant reference/disturbance signals. We propose a new controller parameter optimization approach, which can be carried out experimentally without knowledge of the plant model or the order of the system. The approach has the advantages that controllers can be tuned by perturbing only the initial conditions of the servocompensator, and that the order of the resulting controller can be specified by the designer. Implementation of the proposed controller design approach is described, and an experimental application study of the proposed method applied to a multivariable system with industrial sensor/actuator components is presented to illustrate the feasibility of the design method in an industrial environment.

Tumor-tracking in radiotherapy: parameterization of sensor time-delay compensators and associated performance limitations

Motivated by research into tumour tracking in radiotherapy, this paper considers the problem of constructing a linear time-invariant asymptotic estimator to predict the tumour location in real time. The challenge in the estimator design is to accommodate a time delay associated with the sensor, which in this case is an X-ray imager and associated image processor. The contributions of this paper are first, to show that the class of estimators which achieves perfect asymptotic estimation can be parameterized in a manner similar to the well-known Youla parameterization of stabilizing feedback controllers, and, second, to prove that there are fundamental limits on the performance levels that can be achieved. Aspects of performance considered include disturbance rejection, sensor noise rejection, and sensitivity to model uncertainty. The results are restricted to single-input single-output discrete-time linear time-invariant systems

Performance limitations in control systems with sensor time delays

Abstract This paper derives performance limitations associated with sensor delays in single-input single-output discrete-time feedback loops. Aspects of performance considered are tracking and sensitivity to plant uncertainty. It is shown that, in both one degree-of-freedom and two degree-of-freedom control configurations, closed-loop sensitivity with respect to plant model uncertainty is fundamentally limited by the presense of the sensor delay. The sensitivity bound provided in this paper can be used to quantify how sensitivity necessarily worsens as the sensor delay increases and as the closed-loop bandwidth increases.

Multivariable three-term optimal controller design for large-scale systems

This paper deals with the design of controllers for large-scale linear time-invariant multi-input multi-output systems, such as those that often arise in process control. We focus on two standard controller objectives: (i) asymptotic regulation subject to unmeasurable constant disturbances, and/or (ii) asymptotic tracking of constant set-points. In either case, standard output-feedback controller design methodologies typically result in controllers that have order at least as large as that of the plant; for large-scale systems, the controller order can consequently be impractically large. The purpose of this paper is to introduce, for the subclass of plants that are open-loop stable, a low-order three-term (i.e., PID) multivariable control design approach that is practical to compute numerically, even for large-scale systems. A design algorithm and existence results to construct such a controller are given, and the approach is applied to several examples. Remarkably, at least for the examples considered, the three-term controllers performance is quite similar to that achieved by the standard (much higher order) controller that solves the servomechanism problem

Implementation of stabilizing control laws - How many controller blocks are neede for a universally good implementation?

In this article we investigated three questions. The first question deals with the existence of a universally good implementation of the control law u = Crr - Cyy. This question is answered in the literature, where it is shown that there does exist a universally good three-block implementation. We then turned to the second question, asking whether there exists a universally good implementation that has fewer than three controller blocks. We considered a broad collection of one- and two-block implementations and determined that none of them are good implementations. Consequently, none of the implementations that we considered are universally good. The final question asks whether, for a given plant and control law u = Crr - Cyy, there necessarily exists a good implementation that has fewer than three blocks. Again, based on the example (9)-(12), we conjecture that the answer is no. The overall conclusion of the article is therefore a conjecture, namely, that it is not only sufficient, but sometimes necessary, to use three controller blocks in a good implementation of u = Crr - Cyy

A curve-shaping approach for determining bounds on H/sub /spl infin// performance under hard constraints

Consider an H/sub /spl infin//-norm optimization problem where the goal is to minimize the H/sub /spl infin//-norm of some transfer functions while subject to constraints on, for example, system bandwidth, peak sensitivity, or output variance. This paper presents a method of computing how these constraints limit the achievable performance. The approach involves optimally shaping the sensitivity function magnitude Bode plot.