Mark L. Nagurka

Controlled Impedance Test Apparatus for Studying Human Interpretation of Kinesthetic Feedback

Many feedback control systems, especially those for complex applications, involve humans in the control loop. Visual information traditionally has been presented to human controllers who make manual responses (i.e., via keyboard, joystick, or other interfaces). To expand system bandwidth, other information channels can be presented so human operators. Kinesthesis, the perception of body positions and forces, represents an attractive supplementary form of human-machine communication, since the limbs (e.g., an operators hand) can be used both for input and output of information in the control loop. Although psychophysical studies have measured perception of isolated mechanical properties, limited work has been conducted to study human kinesthetic abilities in the context of control. The research described here assesses judgement of coupled properties, including the superposition of linear stiffness, damping, and inertia. Quantitative perception of these properties may depend upon correct models of the mechanical system with which a user interacts. Similarly, perception of fundamental mechanical properties may be influenced by system delays (on the order of magnitude of human reaction time). This paper describes both an apparatus for understanding kinesthetic interaction with mechanical systems and an approach for studying human perception of mechanical properties.

Leg Motion Analysis During Gait by Multiaxial Accelerometry: Theoretical Foundations and Preliminary Validations

A theoretical formulation for studying limb motions and joint kinetics by multiaxial accelerometry is developed. The technique is designed to study the swing phase of human gait, modeling the lower leg as a rigid body. Major advantages of the approach are that acceleration information needed for the calculation of forces and moments is generated directly, and that the method automatically generates its own initial conditions. Results of validation experiments using both artificial and experimental data demonstrate that the method is theoretically valid, but that it taxes available instrumentation and requires further development before it can be applied in a clinical setting.

Fourier-Based Optimal Control of Nonlinear Dynamic Systems

A method for generating near optimal trajectories of linear and nonlinear dynamic systems, represented by deterministic, lumped-parameter models, is proposed. The method is based on a Fourier series approximation of each generalized coordinate that converts the optimal control problem into an algebraic nonlinear programming problem. The results of computer simulation studies compare favorably to optimal solutions obtained by closed-form analyses and/or by other numerical schemes

Design of PID controllers satisfying gain margin and sensitivity constraints on a set of plants

This paper presents a method for the design of PID-type controllers, including those augmented by a filter on the D element, satisfying a required gain margin and an upper bound on the (complementary) sensitivity for a finite set of plants. Important properties of the method are: (i) it can be applied to plants of any order including non-minimum phase plants, plants with delay, plants characterized by quasi-polynomials, unstable plants and plants described by measured data, (ii) the sensors associated with the PI terms and the D term can be different (i.e., they can have different transfer function models), (iii) the algorithm relies on explicit equations that can be solved efficiently, (iv) the algorithm can be used in near real-time to determine a controller for on-line modification of a plant accounting for its uncertainty and closed-loop specifications, (v) a single plot can be generated that graphically highlights tradeoffs among the gain margin, (complementary) sensitivity bound, low-frequency sensitivity and high-frequency sensor noise amplification, and (vi) the optimal controller for a practical definition of optimality can readily be identified.

Robust PI controller design satisfying sensitivity and uncertainty specifications

This paper presents a control design method for determining proportional-integral-type controllers satisfying specifications on gain margin, phase margin, and an upper bound on the (complementary) sensitivity for a finite set of plants. The approach can be applied to plants that are stable or unstable, plants given by a model or measured data, and plants of any order, including plants with delays. The algorithm is efficient and fast, and as such can be used in near real-time to determine controller parameters (for online modification of the plant model including its uncertainty and/or the specifications). The method gives an optimal controller for a practical definition of optimality. Furthermore, it enables the graphical portrayal of design tradeoffs in a single plot, highlighting the effects of the gain margin, complementary sensitivity bound, low frequency sensitivity and high frequency sensor noise amplification.

Automatic Loop Shaping of Structured Controllers Satisfying QFT Performance

This paper presents a robust noniterative algorithm for the design of controllers of a given structure satisfying frequency-dependent sensitivity specifications. The method is well suited for automatic loop shaping, particularly in the context of Quantitative Feedback Theory (QFT), and offers several advantages, including (i) it can be applied to unstructured uncertain plants, be they stable, unstable or nonminimum phase, (ii) it can be used to design a satisfactory controller of a given structure for plants which are typically difficult to control, such as highly underdamped plants, and (iii) it is suited for design problems incorporating hard restrictions such as bounds on the high-frequency gain or damping of a notch filter. It is assumed that the designer has some idea of the controller structure appropriate for the loop shaping problem.

Simulating Discrete and Rhythmic Multi-joint Human Arm Movements by Optimization of Nonlinear Performance Indices

An optimization approach applied to mechanical linkage models is used to simulate human arm movements. Predicted arm trajectories are the result of minimizing a nonlinear performance index that depends on kinematic or dynamic variables of the movement. A robust optimization algorithm is presented that computes trajectories which satisfy the necessary conditions with high accuracy. It is especially adapted to the analysis of discrete and rhythmic movements. The optimization problem is solved by parameterizing each generalized coordinate (e.g., joint angular displacement) in terms of Jacobi polynomials and Fourier series, depending on whether discrete or rhythmic movements are considered, combined with a multiple shooting algorithm. The parameterization of coordinates has two advantages. First, it provides an initial guess for the multiple shooting algorithm which solves the optimization problem with high accuracy. Second, it leads to a low dimensional representation of discrete and rhythmic movements in terms of expansion coefficients. The selection of a suitable feature space is an important prerequisite for comparison, recognition and classification of movements. In addition, the separate computational analysis of discrete and rhythmic movements is motivated by their distinct neurophysiological realizations in the cortex. By investigating different performance indices subject to different boundary conditions, the approach can be used to examine possible strategies that humans adopt in selecting specific arm motions for the performance of different tasks in a plane and in three-dimensional space.

Fourier-based optimal control approach for structural systems

This paper considers the optimal control of structural systems with quadratic performance indices. The proposed approach approximates each configuration variable of a structural model by the sum of a fifth order polynomial and a finite term Fourier-type series. In contrast to standard linear optimal control approaches which typically require the solution of Riccati equations, the method adopted here is a near optimal approach in which the necessary and sufficient condition of optimality is derived as a system of linear algebraic equations. These equations can be solved directly by a method such as Gaussian elimination. The proposed approach is computationally efficient and can be applied to structural systems of high dimension and/or to structural systems with fixed (or highly penalized) terminal states without numerical difficulties.

A Chebyshev-Based State Representation for Linear Quadratic Optimal Control

A computationally attractive method for determining the optimal control of unconstrained linear dynamic systems with quadratic performance indices is presented. In the proposed method, the difference between each state variable and its initial condition is represented by a finite-term shifted Chebyshev series. The representation leads to a system of linear algebraic equations as the necessary condition of optimality. Simulation studies demonstrate computational advantages relative to a standard Riccati-based method, a transition matrix method, and a previous Fourier-based method

Gain and phase margins of SISO systems from modified root locus plots

Graphically based methods for determining the gain margin and phase margin of linear time-invariant single-input, single-output (SISO) control systems are treated. The gain margin can be found from a graph showing the angle of each closed-loop system eigenvalue in the complex plane as a function of real gain. At any constant real gain, the phase margin can be identified from a graph of the angle of each closed-loop system eigenvalue in the complex plane as a function of gain angle. The proposed methods do not require frequency calculations and highlight the importance of root sensitivity, with the practical design guideline of not selecting control gains that place eigenvalues near break points.<<ETX>>