Martin C. Berg

Multirate digital control system design

Methods for multirate digital control system design are discussed. A simple method for sampling rate selection based on control bandwidths is proposed. Methods for generating a discrete-time state model of a sampled-data plant and a discrete-time equivalent to an analog cost function for a sampled-data plant are described. The successive loop closures and linear quadratic Gaussian synthesis methods are reviewed, and a constrained optimization synthesis method is introduced. The proposed sampling rate selection, discretization, and synthesis methods are applied to two example design problems. Multirate and single-rate compensators synthesized by the different methods are compared based on closed-loop responses with compensators having the same real-time computation load. >

Real-time planning for teams of autonomous vehicles in dynamic uncertain environments

In a highly dynamic environment, an adaptive real-time mission planner is essential for controlling a team of autonomous vehicles to execute a set of tasks. An optimal plan computed prior to the operation will no longer be optimal when the vehicles execute the plan. This dissertation presents a framework and algorithms for solving real-time task and path planning problems by combining Evolutionary Computation (EC) based techniques with a Market-based planning architecture. The planning system takes advantage of the flexibility of EC-based techniques and the distributed structure of Market-based planning. This property allows the vehicles to evolve their task plans and routes in response to the changing environment in real time, and under varying computational time windows.* *This dissertation is a compound document (contains both a paper copy and a CD as part of the dissertation). The CD requires the following system requirements: Windows MediaPlayer or RealPlayer.

Extended Kalman Filtering Applied to a Two-Axis Robotic Arm with Flexible Links

An industrial robot today uses measurements of its joint positions and models of its kinematics and dynamics to estimate and control its end-effector position. Substantially better end-effector position estimation and control performance would be obtainable if direct measurements of its end-effector position were also used. The subject of this paper is extended Kalman filtering for precise estimation of the position of the end-effector of a robot using, in addition to the usual measurements of the joint positions, direct measurements of the end-effector position. The estimation performances of extended Kalman filters are compared in applications to a planar two-axis robotic arm with very flexible links. The comparisons shed new light on the dependence of extended Kalman filter estimation performance on the quality of the model of the arm dynamics that the extended Kalman filter operates with.

Adaptive real-time estimation of end-effector position and orientation using precise measurements of end-effector position

An adaptive estimation method is developed to generate real-time estimates of the position and orientation of the end-effector of an industrial robot and estimates of the root mean squared errors in these estimates, using real-time measurements of the position of a point on the end-effector, in addition to the usual measurements of the joint positions. To compensate for the lack of real-time measurements of the orientation of the end-effector, a Kalman filter is used to update a lookup table model of the kinematics of the robot that most affect the orientation of the end-effector. Measurements of the positions of a point on the end-effector collected during a short sequence of motions of the last axis of the robot are used by the Kalman filter to update this lookup table model. The updated lookup table model, together with real-time measurements of the position of a point on the end-effector and real-time measurements of the joint positions, is used by the estimator to compensate for the effects of geometric errors in the robots structure and temperature variations on the position and orientation of the end-effector. In an application to a six-axis industrial robot, the adaptive estimation method is shown to substantially outperform the direct forward kinematics method whereby the position and orientation of the end-effector are estimated based upon joint position measurements alone.

Pulse Width Control for Precise Positioning of Structurally Flexible Systems Subject to Stiction and Coulomb Friction

Pulse width control refers to the use of a control law to determine the duration of fixed-height force pulses for point-to-point position control of a plant that is subject to mechanical friction, including stiction. The use of constant-gain pulse width control laws for precise positioning of structurally flexible plants subject to stiction and Coulomb friction is analyzed. It is shown that when the plant is a simple two-mass system subject to stiction and Coulomb friction, a position error limit cycle can result. Sufficient conditions for stability and self-sustained oscillation of this closed-loop system are derived. The sufficient conditions for stability are used to determine conditions on the plant parameters and the control gain that guarantee closed-loop stability and thus limit-cycle-free operation and zero steady-state position error. The analysis methods that are introduced are demonstrated in applications to the control of the position of the end-effector of an industrial robot.

Piecewise-Linear-Gain Pulse Width Control for Precise Positioning of Structurally Flexible Systems Subject to Stiction and Coulomb Friction

Pulse width control refers to the use of a control law to determine the duration of fixed-height force pulses for point-to-point position control of a plant that is subject to mechanical friction, including stiction. A quantitative measure of the performance of a pulse width control system is introduced. Applications of this measure suggest that piecewise-linear-gain pulse width control laws will often provide better performance than constant-gain pulse width control laws. A method for designing piecewise-linear-gain pulse width control laws is introduced. The performance measure and piecewise-linear-gain control law design method are demonstrated in applications to the control of the position of the end-effector of an industrial robot.

Reduced-order multirate compensator synthesis

A method for synthesizing reduced order multirate compensators is presented. Necessary conditions for which the compensator parameter values minimize an infinite time quadratic cost function are derived. An algorithm for finding compensator parameter values which satisfy the necessary conditions is described. This algorithm is then used to design several tip position controllers for a two link robot arm.

A new algorithm for multirate digital control law synthesis

A novel algorithm for multirate digital control law synthesis is presented. The algorithm accommodates a generalized controller structure, and all sampling rates for sensor sample-and-hold circuits, digital processor circuits, and control sample-and-hold circuits can be chosen independently. The algorithm uses a gradient-type numerical search to determine the controller matrices so that a finite-time, linear, quadratic, cost function is minimized. The finite time avoids problems with destabilizing sets of controller matrices. To speed the numerical search, closed-form expressions are used to calculate the cost and gradient of the cost with respect to the controller matrices exactly.<<ETX>>

Robustness analysis of a multirate flutter suppression system

A unified approach for analyzing the robustness and performance of multirate systems is presented. The approach is a compilation of existing multirate performance and robustness analysis results, along with some new results, all presented in a consistent state-space formulation. The approach is used to analyze the robustness of a multirate flutter suppression system designed for a model wing. The example highlights some of the practical considerations in multirate performance and robustness analysis.

Design and modeling of a flexible test bed for use in control system analysis and verification

This paper describes a test bed specifically designed for studying the effects of nonlinear friction, backlash, and drive train flexibility on structurally flexible electro-mechanical systems, and for developing control algorithms that will compensate for nonlinear friction, backlash, and drive train flexibility in structurally flexible electro-mechanical systems. The test bed has a modular and adjustable design. Friction, backlash, and flexibility can all be varied or disabled. A mathematical model of the dynamics of the test bed is also described. This model includes stiction, Coulomb friction, backlash and drive train, and link flexibility. The model is verified via comparisons of model-predicted and experimental responses.