Hanz Richter

Modeling nonlinear behavior in a piezoelectric actuator

A piezoelectric tube actuator is employed as a sample positioning device in Nanocut, a cutting instrument conceived to study the mechanics of nanometric cutting. Extension of functionality of the instrument as a nanometric machine tool motivates the search for an accurate model of the actuator for implementing feedback control. A simple nonlinear model describing longitudinal expansion of the piezoelectric tube actuator is presented in this paper. The model derivation is based on a non-formal analogy with nonlinear viscoelastic materials under uniaxial extension, for which the responses to a step input are similar to the piezoelectric tube. Suitability of the model structure for arbitrary inputs is tested by cross-verification between time and frequency domains. Two parameter estimation procedures are examined and the results of the experimental work for characterization, estimation and validation are presented.

A multi-regulator sliding mode control strategy for output-constrained systems

This paper proposes a multi-regulator control scheme for single-input systems, where the setpoint of a regulated output must be changed under the constraint that a set of minimum-phase outputs remain within prescribed bounds. The strategy is based on a max-min selector system frequently used in the aerospace field. The regulators used for the regulated and limited outputs are of the sliding mode type, where the sliding variable is defined as the difference between an output and its allowable limit. The paper establishes overall asymptotic stability, as well as invariance properties leading to limit protection. The design methodology is illustrated with a detailed simulation example on thrust control of a turbofan engine.

Multiplexed Predictive Control of a Large Commercial Turbofan Engine

Model predictive control is a strategy well-suited to handle the highly complex, nonlinear, uncertain, and constrained dynamics involved in aircraft engine control problems. However, it has thus far been infeasible to implement model predictive control in engine control applications, because of the combination of model complexity and the time allotted for the control update calculation. In this paper, a multiplexed implementation is proposed that dramatically reduces the computational burden of the quadratic programming optimization that must be solved online as part of the model-predictive-control algorithm. Actuator updates are calculated sequentially and cyclically in a multiplexed implementation, as opposed to the simultaneous optimization taking place in conventional model predictive control. Theoretical aspects are discussed based on a nominal model, and actual computational savings are demonstrated using a realistic commercial engine model.

Stability of discrete-time systems with quantized input and state measurements

This note focuses on linear discrete-time systems controlled using a quantized input computed from quantized measurements. Nominally stabilizing, but otherwise arbitrary, state feedback gains could result in limit cycling or nonzero equilibrium points. Although a single quantizer is a sector nonlinearity, the presence of a quantizer at each state measurement channel makes traditional absolute stability theory not applicable in a direct way. A global asymptotic stability condition is obtained by means of a result which allows us to apply discrete positive real theory to systems with a sector nonlinearity which is multiplicatively perturbed by a bounded function of the state. The stability result is readily applicable by evaluating the location of the polar plot of a system transfer function relative to a vertical line whose abcissa depends on the one-norm of the feedback gain. A graphical method is also described that can be used to determine the equilibrium points of the closed-loop system for any given feedback gain.

STABLE ROBUST ADAPTIVE IMPEDANCE CONTROL OF A PROSTHETIC LEG

We propose a nonlinear robust model reference adaptive impedance controller for an active prosthetic leg for transfemoral amputees. We use an adaptive control term to consider the uncertain parameters of the system, and a robust control term so the system trajectories converge to a sliding mode boundary layer and exhibit robustness to variations of ground reaction force (GRF). The boundary layer not only compromises between control chattering and tracking performance, but also bounds the parameter adaptation to prevent unfavorable parameter drift. We also prove the stability of the controller for the robotic system in the case of non-scalar boundary layer trajectories using Lyapunov stability theory and Barbalat’s lemma. The acceleration-free regressor form of the system removes the need to measure the joint accelerations, which would otherwise introduce noise in the system. We use particle swarm optimization (PSO) to optimize the design parameters of the controller and the adaptation law. The PSO cost function is comprised of control signal magnitudes and tracking errors. PSO achieves a 8% improvement in the objective function. Finally, we present simulation results to validate the effectiveness of the controller. We achieve good tracking of joint displacements and velocities for both nominal and perturbed values of the system parameters. Variations of ±30% on the system parameters result in an increase of the cost function by only 3%, which confirms the robustness of the controller.Copyright

Robust tracking/impedance control: Application to prosthetics

Stability and human-like motion are among the main factors that should be considered while designing a prosthetic limb. The prosthetic limb should be capable of accommodating environmental forces. The existence of parametric uncertainties has raised the need for robust stability and performance of the prosthesis. In this paper, a mixed tracking/impedance robust controller is developed based on passivity techniques. The controller is developed for general robotic manipulators and then applied to a powered knee/ankle prosthesis model attached to a robotic testing machine. Tracking control is used for the hip and thigh links of the test robot, while impedance control is used for the knee and ankle joints of the prosthesis. The dynamics resulting from the interaction between robot and environment are stabilized by specifying a suitable target impedance. The robust passivity framework was used to derive a joint space controller. A Lyapunov function is used to show that the tracking errors of the motion-controlled joints approach zero, while the impedance of the remaining joints approaches the designed target. A simulation study shows how impedance parameters can be used to trade off reference tracking of the impedance-controlled joints and interaction forces.

Robust Tracking Control of a Prosthesis Test Robot

This paper develops a passivity-based robust motion controller for a robot used in prosthetic leg performance studies. The mathematical model of the robot and passive prosthesis corresponds to a three degree-of-freedom, underactuated rigid manipulator. A form of robotic testing of prostheses involves tracking reference trajectories obtained from human gait studies. The robot presented in this paper emulates hip vertical displacement and thigh swing, and we consider a prosthesis with a passive knee for control development. The control objectives are to track commanded hip displacements and thigh angles accurately, even in the presence of parametric uncertainties and large disturbance forces arising from ground contact during the stance phase. We develop a passivity-based controller suitable for an underactuated system and compare it with a simple independent-joint sliding mode controller (IJ-SMC). This paper describes the mathematical model and nominal parameters, derives the passivity-based controller using Lyapunov techniques and reports success in real-time implementation of both controllers, whose advantages and drawbacks are compared.

Semiactive Virtual Control Method for Robots with Regenerative Energy-Storing Joints

Abstract A framework for modeling and control is introduced for robotic manipulators with a number of energetically self-contained semiactive joints. The control approach consists of three steps. First, a virtual control design is conducted by any suitable means, assuming a fully-actuated system. Then, virtual control inputs are matched by a parameter modulation law. Finally, the storage dynamics are shaped using design parameters. Storage dynamics coincide with the systems internal dynamics under exact virtual control matching. An internal energy balance equation and associated self-powered operation condition are given for the semiactive joints. This condition is a structural characteristic of the system and independent of the control law. Moreover, the internal energy balance equation is independent of the energy storage parameter (capacitance), which adds flexibility to the approach. An external energy balance equation is also given that can be used to calculate the work required from the active joints. A simulation example using a 3-dof prosthesis test robot illustrates the concepts.

Optimal design of a transfemoral prosthesis with energy storage and regeneration

We describe the preliminary optimal design of an electromechanical above-knee active prosthesis with energy storage and regeneration. A DC motor-generator applies a positive or negative torque to the knee. The control system regulates the exchange of energy between the motor-generator and a supercapacitor. The central idea of the design is motivated by the mechanics, energy management, and sensor-based control that constitute human movement. We use biogeography-based optimization, which is an evolutionary algorithm, to optimize the system parameters, and we evaluate its performance with Simulink® models. We optimize three alternative prosthesis designs. Simulation results indicate that the prosthesis can be optimized to achieve knee angle tracking with an RMS error on the order of 0.2 degrees.

A Novel Controller for Gas Turbine Engines with Aggressive Limit Management

A new control scheme is proposed for turbofan engines, where the objective is to transfer a regulated output between two setpoints, with the additional requirement that a set of limited outputs remain within prescribed bounds. The strategy is based on the traditional max-min selector system, replacing linear regulators with sliding mode controllers where the sliding variable for the limited outputs is defined as the difference between the output and its limit. The motivation for the replacement lies in several recently-noted shortcomings associated with the use of linear regulators in the traditional scheme. The proposed technique effectively removes the weaknesses of the traditional scheme. The paper points out these deficiencies and describes the proposed method, establishing overall system stability. The invariance properties leading to limit protection are also elaborated. A design methodology involving a mixed H1=H2 multi-objective feedback gain synthesis is proposed and demonstrated through a design example. Practical applicability is further demonstrated by simulation using a high-fidelity nonlinear engine simulator (C-MAPSS).