Abstract

This project involves the development of an adaptive control algorithm for Computerized Numerical Control machines implemented in a multi-axis motion control board based on a floating-point DSP chip

Introduction

The self-tuning control process involves adaptive modeling of the plant and the application of an inverse controller to enhance the step response of the system.

When the resulting self-tuned inverse controller is applied, the step response of the overall system is improved in terms of shortened rise time while simultaneously avoiding the occurrence of overshoot.

The performance of this solution was verified at three different levels: Software simulation, implementation in a set of isolated motor-encoder pairs, and implementation in a real machine. The use of the adaptive inverse controller effectively improved the step response of the system at all three levels. In the simulation, an ideal response was obtained. In the motor-encoder test, the rise time was reduced by as much as 80%, without overshoot, in some cases. Even with the larger mass of the actual machine, a decrease in the rise time and elimination of the overshoot was obtained in most cases.

I. Results obtained through Software Simulation:

The plant model was used to build an inverse controller that eliminates the effect the plant has over the input signal.  The following figures display the step response with and without the inverse controller:

It is clearly observed that the performance of the system is enhanced by the application of the inverse approach.  The rise time of the system is considerably improved without the inconvenience of large overshoot.

II. Real-Time Results Obtained with a Motor-Encoder Set (No-load Case)

An isolated motor-encoder set was used to test the performance of the algorithm in a real-time environment.  The following figure depicts the model obtained by the combination of the DAC, amplifier, motor, and encoder, in a negative feedback loop configuration: 

The real-time performance of the adaptive algorithm is shown in the following figure:

The rise time of the system using the inverse controller was decreased from 74 samples (without) to only 10 samples.

II. Real-Time Results Obtained with a Machine

The following figure represents the model obtained from one axis of an actual machine:

The performance of the inverse controller in this system is illustrated in the following figure:

Improvement in the step response can be seen after using the inverse controller.   Similar real-time implementations and verifications of the approach demonstrated that it is capable of significantly correcting deficient responses, like the ones shown below :