DeepAI AI Chat
Log In Sign Up

Performance Analysis of Robust Stable PID Controllers Using Dominant Pole Placement for SOPTD Process Models

01/28/2018
by   Saptarshi Das, et al.
0

This paper derives new formulations for designing dominant pole placement based proportional-integral-derivative (PID) controllers to handle second order processes with time delays (SOPTD). Previously, similar attempts have been made for pole placement in delay-free systems. The presence of the time delay term manifests itself as a higher order system with variable number of interlaced poles and zeros upon Pade approximation, which makes it difficult to achieve precise pole placement control. We here report the analytical expressions to constrain the closed loop dominant and non-dominant poles at the desired locations in the complex s-plane, using a third order Pade approximation for the delay term. However, invariance of the closed loop performance with different time delay approximation has also been verified using increasing order of Pade, representing a closed to reality higher order delay dynamics. The choice of the nature of non-dominant poles e.g. all being complex, real or a combination of them modifies the characteristic equation and influences the achievable stability regions. The effect of different types of non-dominant poles and the corresponding stability regions are obtained for nine test-bench processes indicating different levels of open-loop damping and lag to delay ratio. Next, we investigate which expression yields a wider stability region in the design parameter space by using Monte Carlo simulations while uniformly sampling a chosen design parameter space. Various time and frequency domain control performance parameters are investigated next, as well as their deviations with uncertain process parameters, using thousands of Monte Carlo simulations, around the robust stable solution for each of the nine test-bench processes.

READ FULL TEXT

page 16

page 22

page 23

page 34

page 35

page 36

page 37

page 38

10/03/2021

Hybrid Event Shaping to Stabilize Periodic Hybrid Orbits

Many controllers for legged robotic systems leverage open- or closed-loo...
08/25/2020

Loop-shaping for reset control systems – A higher-order sinusoidal-input describing functions approach

The ever-growing demands on speed and precision from the precision motio...
05/30/2020

"Closed Proportional-Integral-Derivative-Loop Model" Following Control

The proportional-integral-derivative (PID) control law is often overlook...
09/28/2020

Frequency-Domain Modelling of Reset Control Systems using an Impulsive Description

The ever-increasing industry desire for improved performance makes linea...
05/25/2021

Surrogate Approximation of the Grad-Shafranov Free Boundary Problem via Stochastic Collocation on Sparse Grids

In magnetic confinement fusion devices, the equilibrium configuration of...