Implementing PID Controller on a hand follower robot using Numerical Methods

TL;DR

The paper addresses stable, precise distance tracking for a hand follower robot by implementing a PID controller via numerical methods. It uses $v = K_p E(t) + K_i \int_0^t E(\tau)d\tau + K_d \dfrac{dE}{dt}$, with the integral approximated by Simpson's rule and the derivative by a backward-difference scheme, embedded in a differential-drive kinematic model in MATLAB. The study demonstrates how careful tuning of $K_p$, $K_i$, and $K_d$ affects responsiveness, overshoot, and steady-state error, identifying a practical set of gains ($K_p=10.8$, $K_i=17.7$, $K_d=3.2$) that achieves stable tracking. The work highlights a viable path to implement PID control with numerical methods for real-time mobile robotics, enabling accurate distance regulation in the presence of disturbances and model uncertainties.

Abstract

Overall, in any system, the proportional term, integral term, and derivative term combined to produce a fast response time, less overshoot, no oscillations, increased stability, and no steady-state errors. Eliminating the steady state errors connected to typical PID systems is crucial for achieving stability. To plot the transfer function's responses with various integrator gains for auto tuning, a MATLAB M-file was developed. Auto tuning techniques were then applied to PID systems to eliminate steady state defects. this paper analyzes and tests the improvement of PID controller over the regular P-controller taking a hand follower robot as a system example using methods with simulation and numerical analysis study.

Figures (8)

• Figure 1: PID control Action
• Figure 2: PID controller output signal
• Figure 3: Differential drive robot
• Figure 4: Derivative and Integral test for sin(x)
• Figure 5: Controller output signal at KP = 5, KI = 17.7 and KD = 3.2