The objective of this paper is a redefinition of the robot control problem, based on realistic (1) models for the industrial robot as a controlled plant, (2) end effector trajectories consistent with manufacturing applications, and (3) the need for end-effector sensing to compensate for uncertainties inherent to most robotic manufacturing applications. Based on extensive analytical and experimental studies, realistic robot dynamic models are presented that have been validated over the frequency range 0 to 50 Hz. These models exhibit a strong influence of drive system flexibility, producing lightly damped poles in the neighborhood of 8 Hz, 14 Hz, and 40 Hz, all unmodeled by the conventional rigid body multiple link robot dynamic approach. The models presented also quantify the significance of nonlinearities in the drive system, in addition to those well-known in the linkage itself. Realistic simulations of robot dynamics and motion controls demonstrate that existing controls coupled with effective path planning produce dynamic path errors that are acceptable for most manufacturing applications. Major benefits are projected, with examples cited, for use of end-effector sensors for position, force, and process control that compensate for uncertainties encountered on the factory floor.

Re-definition of the robot motion control problem: Effects of plant dynamics, drive system constraints, and user requirements

The objective of this paper is a redefinition of the robot control problem, based on (1) realistic models for the industrial robot as a controlled plant, (2) end-effector trajectories consistent with manufacturing applications, and (3) the need for end-effector sensing to compensate for uncertainties inherent to most robotic manufacturing applications. Based on extensive analytical and experimental studies, robot dynamic models are presented that have been validated over the frequency range 0 to 50 Hz. These models exhibit a strong influence of drive system flexibility, producing lightly damped poles in the neighborhood of 8 Hz, 14 Hz, and 40 Hz, all unmodeled by the conventional rigid-body multiple-link robot dynamic approach. The models presented also quantify the significance of non-linearities in the drive system, in addition to those well known in the linkage itself. Simulations of robot dynamics and motion controls demonstrate that existing controls coupled with effective path planning produce dynamic path errors that are acceptable for most manufacturing applications. Major benefits are projected, with examples cited, for use of end-effector sensors for position, force, and process control.

Redefinition of the robot motion-control problem

Nonlinear proportional-integral-derivative (NPID) control is implemented by varying the controller gains as a function of system state. NPID control has been previously described and implemented, and recently a constructive Lyapunov stability proof has been given. Here, NPID control analysis and design methods are extended to tracking, and to systems with state feedback and integral control. Experimental results are presented showing improved tracking accuracy and friction compensation by NPID control.

New results in NPID control: Tracking, integral control, friction compensation and experimental results

In this report, some 40 papers related to backlash control have been studied, and their results have been arranged into a systematic structure, where the main categories are linear, passive and act ...

A literature survey on control of automotive powertrains with backlash

Nonlinear PID (NPID) control is implemented by allowing the controller gains to vary as a function of system state. NPID control has been previously described and implemented, and recently a constructive Lyapunov stability proof has been given. The controllers arising with the constructive Lyapunov method will in general depend on knowledge of the full state vector. In the present work, NPID controllers that operate without knowledge of some state variables are demonstrated. A general but conservative design method is presented with an experimental demonstration. For a special case, complete necessary and sufficient conditions are established; for this case, simulation of a robotic force control application demonstrates well-damped control with no requirement for a force-rate signal. The extension to cases of partial state knowledge is important for NPID control, which is most practical when some state variables—particularly rate variables—are poorly known, confounding full-state feedback or other high-da...

Nonlinear PID Control with Partial State Knowledge: Damping without Derivatives:

We describe a new nonlinear compensator synthesis approach and illustrate it with an application to a position servo design problem from robotics. The synthesis technique is based on a set of amplitude-dependent sinusoidal-input describing function (SIDF) models of the nonlinear plant. An intermediate step is the design of a linear compensator set based on these models; final synthesis of the nonlinear control system is accomplished by SIDE inversion to determine the required compensator nonlinearities. The major extension in comparison with earlier research is that the compensator so obtained is fully nonlinear; i.e., there is a nonlinear operator associated with each term (proportional, integral, derivative) in the compensator. This approach is capable of treating nonlinear plants of a very general type, with no restrictions as to system order, number of nonlinearities, configuration, or nonlinearity type, and can be extended readily to include other compensator types, e.g., lead/lag. The end result is a closed-loop nonlinear control system that is relatively insensitive to reference input amplitude.

Nonlinear Compensator Synthesis via Sinusoidal-Input Describing Functions

In this paper, we report on recent progress in developing nonlinear control system design techniques based on sinusoidal-input describing function (SIDF) methods. Primarily, this involves illustrating a fundamental difference between SIDF and random-input describing function (RIDF) models of nonlinear systems, developing the nonlinear controller design method more fully, and demonstrating it by applying it to a significant nonlinear control design problem in robotics. Based on these results, the use of this nonlinear controller design method should be substantially better understood.

Kevin L. Strobel

Papers

Nonlinear Compensator Synthesis via Sinusoidal-Input Describing Functions

Applications of a Nonlinear Controller Design Approach based on Quasilinear System Models