Christian Endisch

Contributions to non-identifier based adaptive control in mechatronics

Funnel-Control (FC)-an adaptive (time-varying) MIMO/SISO control strategy-is re-introduced and its applicability introductory for position control of nonlinear, coupled (rigid) robotic systems and for speed control of nonlinear two-mass flexible servo systems is shown. Additionally Error Reference Control (ERC)-a direct derivative of FC-is established. ERC is specially designed with asymmetric boundaries and auxiliary reference, ensuring that the control error evolves within a prespecified tube (a shrinked funnel region, achieving even better tracking performance). FC and hence ERC are based on the high-gain stabilizability of minimum-phase systems with relative degree one and known sign of the high-frequency gain. Although the plant only needs to be known in structure, both concepts assure prescribed transient behavior without identification and/or parameter estimation. As most industrial applications, also the considered robotic and two-mass flexible servo systems, exhibit relative degrees greater than one, FC and ERC cannot directly be applied. Therefore a special state feedback is introduced, reducing the relative degree and retaining the minimum-phase property. The additional implementation of a nominal PI-like extension guarantees good disturbance rejection and asymptotic tracking of (constant) velocity and position reference trajectories. Simulation results for a 6-DOF Manutec r3 robot underpin and compare the achievable position control performance of one overall MIMO Funnel Controller for all joints and one SISO Funnel Controller for each joint (6 controllers). For nonlinear two-mass flexible servo systems, measurement results demonstrate the achievable load speed control performance of FC and ERC in comparison to optimal LQ state feedback.

Funnel-Control in robotics: An introduction

An adaptive (time-varying) MIMO/SISO control strategy - funnel-control - for position control of nonlinear, coupled (rigid) robotic systems is presented and its applicability in robotics introductory shown. The concept is based on the high-gain controllability of minimum-phase systems with relative degree one and known high-frequency gain. The approach allows prescribed transient behavior without identification and/or parameter estimation, although the plant is only structurally known. As most industrial applications - also the considered robotic systems - exhibit higher relative degrees, funnel-control is not directly applicable. Therefore a state-feedback like extension is introduced, which permits the reduction of the relative degree and retains the minimum-phase property. The additional implementation of a Pi-like structure assures good disturbance rejection and asymptotic tracking of the reference position trajectory. Simulation results for a 6-DOF Manutec R3 robot show the achievable performance of one overall MIMO Funnel Controller for all joints and one SISO funnel controller for each joint (6 controllers).

Levenberg-marquardt-based OBS algorithm using adaptive pruning interval for system identification with dynamic neural networks

This paper presents a pruning algorithm using adaptive pruning interval for system identification with general dynamic neural networks (GDNN). GDNNs are artificial neural networks with internal dynamics. All layers have feedback connections with time delays to the same and to all other layers. The parameters are trained with the Levenberg-Marquardt (LM) optimization algorithm. Therefore the Jacobian matrix is required. The Jacobian is calculated by real time recurrent learning (RTRL). As both LM and OBS need Hessian information, computing time can be saved, if OBS uses the scaled inverse Hessian already calculated for the LM algorithm. This paper discusses the effect of using the scaled Hessian instead of the real Hessian in the OBS pruning approach. In addition to that an adaptive pruning interval is introduced. Due to pruning the structure of the identification model is changed drastically. So the parameter optimization task between the pruning steps becomes more or less complex. To guarantee that the parameter optimization algorithm has enough time to cope with the structural changes in the GDNN-model, it is suggested to adapt the pruning interval during the identification process. The proposed algorithm is verified simulatively for two standard identification examples.

Optimal brain surgeon for general dynamic neural networks

This paper presents a pruning algorithm based on optimal brain surgeon (OBS) for general dynamic neural networks (GDNN). The pruning algorithm uses Hessian information and considers the order of time delay for saliency calculation. In GDNNs all layers have feedback connections with time delays to the same and to all other layers. The parameters are trained with the Levenberg-Marquardt (LM) algorithm. Therefore the Jacobian matrix is required. The Jacobian is calculated by real time recurrent learning (RTRL). As both LM and OBS need Hessian information, a rational implementation is suggested.

Comments on "Backpropagation Algorithms for a Broad Class of Dynamic Networks

In a recent paper, De Jesús proposed a general framework for describing dynamic neural networks. Gradient and Jacobian calculations were discussed based on backpropagation-through-time (BPTT) algorithm and real-time recurrent learning (RTRL). Some errors in the paper of De Jesús bring difficulties for other researchers who want to implement the algorithms. This comments paper shows the critical parts of the publication and gives errata to facilitate understanding and implementation.

Error Reference Control of nonlinear two-mass flexible servo systems

This paper recapitulates the adaptive (time- varying) control strategy funnel-control (FC) and introduces its direct derivative error reference control (ERC) with specially designed Funnel boundaries and auxiliary reference. Both controller designs are comparatively applied to a nonlinear two-mass flexible servo system for speed control. ERC (as derivative of FC) is based on the high-gain controllability of minimum-phase systems with relative degree one and known high-frequency gain. Both implementations allow prescribed transient behavior without identification and/or parameter estimation, although the plant is only structurally known (huge parameter deviations are tolerated). As most industrial applications - also the considered two-mass system - exhibit higher relative degrees, the control strategy is not directly applicable. Therefore a state-feedback like extension is introduced, which assures the reduction of the relative degree and the minimum- phase property. By an additional implementation of a Pi-like structure, disturbance rejection and asymptotic tracking of the load speed for a given time-varying velocity trajectory is achieved. Measurement results underpin the achievable performance.

Parameter Identification of a Nonlinear Two Mass System Using Prior Knowledge

This article presents a new method for system identification based on dynamic neural networks using prior knowledge. A discrete chart is derived from a given signal flow chart. This discrete chart is implemented in a dynamic neural network model. The weights of the model correspond to physical parameters of the real system. Nonlinear parts of the signal flow chart are represented by nonlinear subparts of the neural network. An optimization algorithm trains the weights of the dynamic neural network model. The proposed identification approach is tested with a nonlinear two mass system.