Accurate control of reciprocal ratation of digital servo

Hello, friends.

Recently, I try to control a digital servo to realize reciprocal rotation with a frequency of 2-4Hz and an amplitude of 30 degrees. The ratation follow the sine curve. Unfortunately the servo has no feedback and the load is quite large, which results in low accuracy.

Are there any methods to this problem? Is it possible to use PID control?

Waiting for your precious suggestions!!!

Is it possible to use PID control?

Given an encoder or other sensor, then yes, in principle, although you'd be using one loop to drive the servo's
built-in loop, which isn't ideal.

But first its a good idea to figure out what accuracy you actually need.

load is quite large, which results in low accuracy.

Use a servo better suited for the load.

There maybe better ways to do this , such as with a conventional motor and linkage to rock the weight .

Scotch linkage?
Bell crank ?

groundFungus:
Use a servo better suited for the load.

A proper servomotor springs to mind as the way to do this - direct drive and high performance
control loops.

[ Have to link to this amazing video again (demonstrating high end servomotor
performance - despite the awful voice over and "nano millimeters" reference!)
https://www.youtube.com/watch?v=1F4-plhdnj0 ]