Bongsu Hahn

Modeling and Optimal Low-Power On–Off Control of Thin-Film Piezoelectric Rotational Actuators

A novel open-loop minimal energy on-off servo system and control strategy are described for ensuring specified displacements from new microscale piezoelectric rotational joints under extremely strict power budgets. The rotational joints are driven by thin-film lead-zirconate-titanate actuators and are targeted for use in autonomous terrestrial microrobots. A lumped-parameter, second-order model of anticipated joint behavior is utilized to estimate the natural frequency and damping ratio of the robot joints, which, in turn, are used to identify necessary sampling rates and switching drive circuit parameters for implementation of on-off control. An identified model of leg joint behavior is then used to both verify lumped-parameter modeling and to optimize on-off input sequences to the rotary joint. The optimization procedure incorporates energy costs from both switching and holding an input voltage on microactuators that behave as a capacitive load, while ensuring that specified final states of a dynamic system are achieved at a specified point in time. Optimization is done via a new application of binary programming. In addition, modest robustness of the system response to parameter variation can be produced during control sequence generation. Optimized input sequences are applied to both macroscale piezoelectric actuators and to prototype thin-film piezoelectric leg joints, and show that specified actuator motions can be achieved with energy consumption of less than 5 μJ per movement.

A Model-Free ON–OFF Iterative Adaptive Controller Based on Stochastic Approximation

A model-free on-off iterative adaptive controller is described for application to microscale servo systems performing repeated motions under extremely strict power constraints. The approach is motivated by the needs of piezoelectric actuators in autonomous microrobots, where power consumption in analog circuitry and/or for position sensing may be much larger than that of the actuators themselves. The control algorithm adjusts switching instances between “on” and “off” inputs to the actuator to minimize an objective function using simultaneously perturbed stochastic approximation of the gradient with just a single sensor measurement in each iteration. Convergence conditions for the gradient approximation are shown to apply when the possibility for a range of possible switching times minimizing the objective function is accounted for, while a method is proposed for avoiding local minima for plants with bounded nonlinearities. The algorithm is tested on a prototype piezoelectric microactuator.

On-off control for low-power servo control in piezoelectric micro-robotics

Autonomous micro-systems require extremely strict power budgeting to provide useful battery lifetime and functionality. To produce bio-inspired terrestrial micro-robots, this power budget must encompass servo control of a set of robotic leg joints. Piezoelectric actuators can provide high-force actuation necessary for such an application, but driving circuitry for piezoelectric actuator control can consume excessive power. On-off control can reduce actuator power consumption by eliminating analog amplification and minimizing the number of on-off transitions required to perform a given leg joint motion, as compared to conventional PWM controllers. A sample on-off controller designed to require a limited number of on-off transitions from a prototype system is described, and trade-offs to motion accuracy and robustness as power consumption is reduced are discussed. Experimental tests are conducted on a macro-scale piezoelectric test-bed.Copyright

Sensing parameter selection for ultra-low-power system identification

In micro-scale electromechanical systems, power to perform accurate position sensing often greatly exceed the power needed to generate motion. This paper explores the implications of sampling rate and amplifier noise density selection on performance of a system identification algorithm using a capacitive sensing circuit. Specific performance objectives are to minimize or limit convergence rate and power consumption to identify dynamics of a rotary micro-stage. A rearrangement of the conventional recursive least-squares identification algorithm is performed to make operating cost an explicit function of sensor design parameters. It is observed that there is a strong dependence of convergence rate and error on sampling rate, while energy dependence is driven by error that may be tolerated in final identified parameters.

Coordinated voltage conversion and low-power micro-actuator switching

Due to very low power throughput and behavior as primarily capacitive loads, voltage conversion for micro-scale piezoelectric and electrostatic actuators can be very inefficient, while analog drive circuit supply currents may also exceed actuator power consumption. When limited instead to switching commands at discrete time instants to control micro-actuator motion, it may be advantageous to coordinate operating periods of any voltage conversion circuitry with actuators. A sample scenario of a traditional boost converter driving a thin-film piezoelectric micro-robotic appendage along a trajectory is considered through simulation studies. Some ranges of target motion accuracy are achieved using less energy, up to a 25% reduction at 30 V, for a 4 V battery, when coordinating voltage converter operation, even when conversion efficiency is very low.Copyright

A model-free on-off iterative adaptive controller based on stochastic approximation

An on-off iterative adaptive controller has been developed that is applicable to servo systems performing repeated motions under extremely strict power constraints. The motivation for this approach is the control of piezoelectric actuators in autonomous micro-robots, where power consumption in analog circuitry and/or for position sensing may be much larger than that of the actuators themselves. The control algorithm optimizes the switching instances between ‘on’ and ‘off’ inputs to the actuator using a stochastic approximation of the gradient of an objective function, namely that the system reach a specified output value at a specified time. This allows rapid convergence of system output to the desired value using just a single sensor measurement per iteration and discrete voltage inputs.

Low-power switching control schemes for piezoelectric micro-robotic actuators

This article describes the development of piezoelectric micro-actuators for use in micro-robotic systems, and surveys controllers and power electronics for such actuators to meet power limitations of terrestrial micro-robots with high mobility. A thin-film lead-zirconate-titanate lateral actuator design with one micron stroke and several millinewtons of actuation force is described, and sample experimental results provided. A method for integrating these actuators with flexible silicon micro-structures, and implications for micro-robotic pay-load capacity are presented. On-off control is proposed as a method to minimize energy usage by piezoelectric actuators and driving circuitry when moving a micro-robotic appendage based on these designs. Low efficiency of voltage converters and large power consumption of sensing circuitry are identified as barriers to further enhancing servo capabilities of bio-inspired terrestrial micro-robots.Copyright

Convergence and Energy Analysis for Iterative Adaptive ON-OFF Control of Piezoelectric Microactuators

A technique is presented for estimating the number of iterations needed for convergence of iterative adaptive ON-OFF controllers to optimal switching times, for certain controllers proposed for managing stepping motion in autonomous microrobots. An upper bound on output error as a function of error in ON-OFF switching times is obtained, and lower bounds on the change in switching times from iteration-to-iteration are used to estimate output error evolution. The simulation and experimental results from the test case of a piezoelectric microrobotic leg joint indicate reasonable agreement between estimated and actual error. The use of convergence estimates to improve controller design with respect to total energy consumption is then described.

Model-Free Adaptive On-Off Step Controller for Piezoelectric Micro-Robots

An adaptive, model-free on-off controller is described for situations in which a desired step response is to be repeated many times, but there is incomplete information available about the system dynamics. The controller adapts a set of on-off switching transition times as a function of certain objective measurements defined by the designer. While the controller does not utilize any model of the system to perform this adaptation, the effects of the adaptation on known plants can be analyzed to find a range of systems for which the on-off switching times will result meeting desired objectives. This analysis is applied to lightly-damped 2nd -order systems representative of micro-robotic leg joints driven by piezoelectric actuators, and used to identify on-off switching frequencies, sensing frequencies, and adaptation parameters that converge for many plants. This can produce a controller with good robustness to system variation and relatively low switching and sampling frequencies, which can keep power consumption of for piezoelectric servo control very low.Copyright

Low-Power Control Strategies for Thin-Film Piezoelectric Micro-Robotic Actuators

Three low-power control strategies for piezoelectric actuators based on on-off or related switching control approaches are described. These strategies are targeted for leg actuation in autonomous micro-robots, where available power is severely constrained, below the power level that more conventional analog or pulse-width-modulation drive circuitry, switching rates, and/or sampling frequency would require. The first strategy optimizes the sequence of ‘on’ and ‘off’ transitions over a finite number of steps to minimize actuator energy while ensuring that a system moves to a desired set of final states. Transitions are selected via convex optimization by binary programming. The second strategy optimizes a set of commands to a drive circuit including charge recovery components to improve both power consumption and positioning accuracy, with optimal transitions chosen using mixed integer quadratic programming. The third strategy is proposed to account for modeling error using step to step adaptation of input sequences with limited sensor measurements.Copyright