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In micro-scale electromechanical systems, the power to perform accurate position sensing often greatly exceeds the power needed to generate motion. This paper explores the implications of sampling rate and amplifier noise density selection on the 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 the 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 the sampling rate, while energy dependence is driven by error that may be tolerated in the final identified parameters.

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.

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.

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 novel model-free iterative adaptive controller is presented for lowpower control of piezoelectric actuators. The controller uses simple adaptation rules based on known general behavior of piezoelectric actuators to adjust onoff switching times to drive piezoelectric actuators through a desired transient step motion. Adaptation rules are based on small numbers of measurements taken during each iteration of the actuator movement. Combined with the use of only on-off control inputs, controller implementation can be possible at much lower overall power levels than would be needed to implement a conventional control strategy such as through pulse-width-modulation (PWM) with real-time feedback. Such power savings are particularly important for the intended controller application to piezoelectric microactuators driving autonomous terrestrial micro-robots. A method for predicting convergence of systems with nominally linear dynamics and unknown, bounded nonlinearities is described, and applied to a sample target piezoelectric actuator. The controller is tested in simulation and experimentally on a piezoelectric cantilever actuator, and shows predicted convergence to the desired response.

Autonomous microsystems often operate under both strict power and energy constraints and substantial environmental variation. To improve sensing and control performance, parameter identification techniques can be useful if they may be implemented within an appropriate power budget. While it is well known that identification algorithm performance depends on sampling rate, for energy minimization sensor power models and rates of parameter adaptation can also significantly influence optimal sensor usage. In this paper, an empirical, simulation-generated model is found for parameter error of recursive least square identification of a prototypical second-order linear continuous system as a function of sampling rate, number of samples, and sensor noise density. This model is coupled with representative power models of certain common sensing circuits used in microelectromechanical systems (MEMS) to recommend optimal sensing schemes for low-power parameter identification. A case study of a walking micro-robot is presented.

Iterative adaptive on-off control is a potential control strategy for ultra-low-power control of micro-actuators that behave as capacitive loads. Such an approach allows for relatively low sensor sampling frequencies and the use of simple switched inputs, which can be implemented at lower power levels than control with analog inputs and real-time feedback. A technique is presented for estimating the convergence time of an on-off controller proposed for controlling stepping motion in autonomous micro-robots. Error in measured outputs at each iteration are estimated using upper bounds on output error as a function of error in on-off switching times and lower bounds on the change in on-off switching times from iteration to iteration. While a strict upper bound on error is not provided by the final error estimator, simulation and experimental results from the test case of a piezoelectric micro-robotic leg joint indicate reasonable agreement between estimated error and full controller behavior. Convergence estimates may then be used to improve controller design with respect to total energy consumed.© 2012 ASME

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 © 2011 by ASME

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 © 2009 by ASME

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 © 2009 by ASME

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 © 2008 by ASME and US Government

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 © 2008 by ASME