A. Haraldsdottir

Bio: A. Haraldsdottir is an academic researcher from University of Michigan. The author has contributed to research in topics: Discrete time and continuous time & Linear system. The author has an hindex of 2, co-authored 3 publications receiving 21 citations.

Sensitivity reduction by state derivative feedback.

Abstract: This paper shows that the sensitivity of state feedback control systems can be re­ duced by additional state derivative feedback, for a fixed closed loop eigenstructure. The price of this sensitivity reduction is in general noise response amplification. Two indices which quantify stability robustness and response sensitivity are given for time invariant continuous time and discrete time systems, together with an index of response to disturbances and noise. Closed form expressions for the gradients of these indices are given. A two step design procedure is proposed which consists of first selecting a closed loop eigenstructure, then minimizing one of the sensitivity in­ dices under a magnitude constraint on the noise response. Examples are given to il­ lustrate this original design procedure.

Control of Linear Systems by Output Proportional Plus Derivative Feedback

Abstract: A design procedure for systems using proportional plus derivative output feedback for continuous and discrete time systems is presented. A performance index was developed that represents two major goals, regulation and sensitivity. Plant disturbances and measurement noise effects were quantified, as well as two sensitivity measures, eigenvalue sensitivity and response sensitivity. Several example problems were presented to illustrate the proposed design method

Control of Linear Systems by Output Proportional Plus Derivative Feedback

Abstract: This paper presents a control design procedure for linear time invariant systems using output proportional plus derivative feedback. The traditional linear quadratic performance index is used with additional terms to penalize disturbance and noise response and eigenvalue and response sensitivities. The sensitivity terms represent measures of stability robustness. It is shown that the derivative feedback improves the measure of performance. This design procedure has been applied to obtain an improved autopilot for the lateral dynamics of an L1011 aircraft.

Time-Delayed Control of SISO Systems for Improved Stability Margins

Abstract: While time delays typically lead to poor control performance, and even instability, previous research shows that time delays can, in some cases, be beneficial. This paper presents a new benefit of time-delayed control (TDC) for single-input single-output (SISO) linear time invariant (LTI) systems: it can be used to improve robustness. Time delays can be used to approximate state derivative feedback (SSD), which together with state feedback (SF) can reduce sensitivity and improve stability margins. Additional sensors are not required since the state derivatives are approximated using available measurements and time delays. A systematic design approach, based on solution of delay differential equations (DDEs) using the Lambert W method, is presented using a scalar example. The method is then applied to both single- and two-degree of freedom (DOF) mechanical systems. The simulation results demonstrate excellent performance with improved stability margins. [DOI: 10.1115/1.4028528]

Positive real control for descriptor systems with uncertainties in the derivative matrix via a proportional plus derivative feedback

Abstract: This article deals with the problem of normalisation and positive real control synthesis for a class of descriptor systems with uncertainties in the derivative matrix. Attention is focused on the design of a proportional plus derivative PD state feedback, which guarantees that the closed-loop system is quadratically normal and quadratically stable QNQS and the closed-loop transfer function is extended strictly positive real ESPR. We first present a new linear matrix inequality LMI characterisation of positive realness for normal descriptor systems. This new characterisation provides a kind of decoupling among the Lyapunov matrix, the system matrix and the derivative matrix. Based on this, a necessary and sufficient condition for the desired PD controllers is given and a PD controller is constructed by solving LMIs. Finally, a numerical example is given to demonstrate that the proposed method is effective.

Dynamic control modification techniques in teleoperation of a flexible manipulator

Abstract: The objective of this research is to reduce the end-point vibration of a large, teleoperated manipulator while preserving the usefulness of the system motion. A master arm is designed to measure desired joint angles as the user specifies a desired tip motion. The desired joint angles from the master arm are the inputs to an adaptive PD control algorithm that positions the end-point of the manipulator. As the user moves the tip of the master, the robot will vibrate at its natural frequencies which makes it difficult to position the end-point. To eliminate the tip vibration during teleoperated motions, an input shaping method is presented. The input shaping method transforms each sample of the desired input into a new set of impulses that do not excite the system resonances. The method is explained using the equation of motion for a simple, second-order system. The impulse response of such a system is derived and the constraint equations for vibrationless motion are presented. To evaluate the robustness of the method, a different residual vibration equation from Singer's is derived that more accurately represents the input shaping technique. The input shaping method is shown to actually increase the residual vibration in certain situations when the system parameters are not accurately specified. Finally, the implementation of the input shaping method to a system with varying parameters is shown to induce a vibration into the system. To eliminate this vibration, a modified command shaping technique is developed. The ability of the modified command shaping method to reduce vibration at the system resonances is tested by varying input perturbations to trajectories in a range of possible user inputs. By comparing the frequency responses of the transverse acceleration at the end-point of the manipulator, the modified method is compared to the original PD routine. The control scheme that produces the smaller magnitude of resonant vibration at the first natural frequency is considered the more effective control method.