Rüdiger Neumann

A flatness based design for tracking control of pneumatic muscle actuators

Because of their high power/weight ratio pneumatic actuators, especially the so called pneumatic muscles, are very interesting for the use as actuators in robotics. But, in fact the physical model is highly nonlinear, in the following a flatness based position controller for the pneumatic artificial muscles is presented. The considered pneumatic muscle is produced by the manufacturer Festo and possesses a high pulling force to 4000N and a very long lifetime at least to 10 million switching cycles. The control objective is to track the payload along a specified reference path including an active attenuation. Since a model based control approach is pursued, a physical model is presented for an experimental setup. The model is very nonlinear making nonlinear flatness based control desirable. Experimental results are included and demonstrate the efficiency of the control.

Optimal System Design of SISO-Servopneumatic Positioning Drives

Servopneumatic actuators are very attractive for automated handling tasks or robot operations. They have many advantages such as high speed, high robustness in rough manufacturing environment or high power-to-weight ratio. The considered actuator system is a standard configuration in pneumatics consisting of a double acting pneumatic cylinder controlled by a proportional directional control valve. For the set-up a detailed mathematical model is derived. In order to guarantee an accurate tracking behaviour, a model-based nonlinear controller is presented. Model based approaches for the control design have several advantages. Tuning of the controller can be reached in a systematic way even in the case of a large variety of different configurations. But not only the control design itself can be treated. The model offers the possibility to optimize the size of components for demanded automation tasks. In most cases, this is solved based on steady state assumptions. In this contribution, a method for a design procedure for the pneumatic actuator system based on the dynamic equation is presented. With the representation of the system, an optimization procedure for the components is introduced. The optimization criteria consist of the minimization of the air consumption and investment costs.

Model-based feedforward position control of constant curvature continuum robots using feedback linearization

Fast and exact motions of continuum robots are hardly seen so far. Partly this is caused by physical constraints, e.g. small available actuation forces. Another reason is the dynamic coupling between the actuators that cannot be neglected during fast motions. Therefore, a model-based MIMO controller in actuator space was developed, that is based on a spatial dynamic model with one mass point per section. Using feedback linearization, the actuators can be decoupled and feedforward control in combination with linear controllers can be applied. Measurements of an example manipulator show the good tracking result of pure feedforward action with feedback linearization. Adding a linear PD-controller increases the robustness against disturbances without reducing the possibility of fast motions.

Dynamic modeling of constant curvature continuum robots using the Euler-Lagrange formalism

Dynamic models of continuum manipulators tend to become very complex, especially for spatial manipulators with multiple sections. Therefore a practicable model is needed that can be used for simulations and model-based control design. Neglecting rotational energies and assuming a continuum manipulator that consists of a single concentrated mass per section, dynamic equations for each actuator state are derived using the Euler-Lagrange formalism. Forces, positions and velocities are transformed to a global reference system using the homogeneous transformation based on constant curvature robot kinematics and its derivatives. Measurements of an example manipulator verify the resulting dynamic model that can be used to both simulate the dynamics and calculate the inverted robot dynamics needed for model-based controller design.

Distributed Parameter Modeling of Flexible Ball Screw Drives Using Ritz Series Discretization

Ball screw drives are used in automation applications and machine tools to translate rotational motion of an electric motor into translational motion of a slide. Their frequency responses show characteristic torsional and translational resonances. The resonance frequencies vary with the slide position, which is due to the distributed stiffness and inertia of the flexible ball screw. The proposed model treats the ball screw as a flexible element, using Ritz series expansions to obtain a finite approximation of the continuous deformations. The use of problem-specific basis functions allows for a low-order approximation, making the model especially well suited for control design. The model shows excellent validation results and reproduces the variation of the resonance frequencies with high accuracy.

Energy efficient use of compressed air in pneumatic drive systems for motion tasks

This paper discusses the possibilities of an energy efficient use of compressed air in pneumatic drives such as cylinders in combination with switching valves. It presents a numerical optimization realization with which an energy optimal open loop control of standard pneumatic systems with switching valves is derived. The main part of air savings results from a better usage of the energy stored in the compressed air namely the expansion energy. It is shown that savings could be done up to 85% depending on the application. The optimization results are validated with measurements and are compared to standard pneumatic control of cylinders.

Online TCP trajectory planning for redundant continuum manipulators using quadratic programming

Continuum manipulators enable new fields of application by their inherent flexibility and continuous deformations. However, they cannot compete with conventional robots yet. This is partially caused by a lack of practical and powerful trajectory generation algorithms. Therefore, an online TCP trajectory generator for redundant continuum manipulators has been developed, that computes desired actuator states for given task variables that can be used for actuator controllers. Using the fast gradient optimization algorithm and quadratic programming, actuator velocities are optimized considering actuator constraints with respect to a cost function including the differential kinematics. Experiments prove the online capabilities of the proposed trajectory generation approach. Furthermore, the presented method can be used for controlling continuum robots by incorporating inputs from human-machine-interaction devices.

Dimensioning of pneumatic cylinders for motion tasks

This paper proposes a novel method for dimensioning pneumatic cylinders for motion tasks. Considered are standard pneumatic cylinders with common directional control valves and exhaust flow throttles. The focus thereby is on the dimensioning of the cylinders for point-to-point motions regarding energy efficiency. The proposed strategy is based on the eigenfrequency and considers similarity transformations. The dimensioning of the cylinder diameter and the valve conductance bases upon a few algebraic equations leading to optimally sized pneumatic cylinders. Furthermore, the equations are used for classification purposes of the pneumatic cylinders regarding energy efficiency.

Flatness-based MIMO control of hybrid stepper motors - design and implementation

Hybrid stepper motors are often used as actuators in automation and handling. To overcome their main drawbacks, step-wise motion and poor robustness against load disturbances, closed loop control can be applied. The concept of differential flatness offers powerful tools for a wide range of linear and nonlinear systems. The differential flatness property of the nonlinear MIMO model of a hybrid stepper motor is proven and a flat output is determined constructively as solution to a set of partial differential equations. By use of the flat output, an asymptotic tracking control is designed and evaluated in simulation and experiments.

Modellierung von Hybrid-Schrittmotoren für den optimierten, geregelten Betrieb

Zusammenfassung Hybrid-Schrittmotoren im geregelten Betrieb stellen für einfache Anwendungen eine Alternative zu teuren Servomotoren dar. Für den Reglerentwurf wird ein Modell benötigt, das die Besonderheiten der Hybrid-Schrittmotoren berücksichtigt. In diesem Beitrag wird ein Modell hergeleitet, das die Effekte der ausgeprägten Pole berücksichtigt. Wichtige Modellparameter werden dabei durch Minimierung des quadratischen Fehlers bestimmt. Das Modell zeigt hohe Übereinstimmung mit Experimenten und kann zur Optimierung des Servobetriebs hinsichtlich Energieverbrauch und Drehmoment genutzt werden.