Hi. Interesting question, I hope you don't expect a simple answer!

The answer is entirely depending on your definition of "best". PI requires very little resources; just the error signal, one memory cell and a few mathematical operations. Other controllers may perform better, given some definition of better (faster, more accurate, less power, ...) but will most certainly require more computation and more storage.

Comparisons of different controllers can probably be found in the literature.

Olof

Yes, interesting question.

No, PI is not the best controller. It is only the most common controiller, because many, or maybe even most, applications are simple and do not need too much.

You just close a loop with some proportional gain P and the closed-loop may happen to already be stable. If you try to incrrease the gain to make the system faster, you start "discovering" oscillatons, nonlinearities, etc., which would ask you to do some real analysis of your  system and to start designing some real controller. Or... you decide to be satisfied with what the not-too large P can give.

Then why the integral I? Because, without high DC gain, you get a nonzero steady-state error. The integral gain gives infinite dc gain, which forces the  steady state error to go to zero.

However, again, if you try to get faster, you discover oscillations that require damping and this is the role of the derivative component D. 

You may also find out that adding the acceleration component A may also positively affect perrfromance, but this not only depends on what you call "best," but also on  what kind of system you have to deal with. 

Hi Ms. Mariam,

Searching for the best controller and asking whether PI controller is the best one, are two separate issue, which need to be investigated. You probably think that the PI controller is a probable contender for being the best controller. Otherwise, you couldn't have asked this question in the first place. More importantly, what makes you think so?

Since your supervisor hinted at the PIDA controller, s/he probably also thinks that the PIDA controller is a probable contender for being the best controller and wants you to carry out the investigation.

The so-called “best controller” needs to be considered in the contexts of the kind of system you have to deal with, the model dependency, the performance criteria, the system constraints, the design contingency, the computational complexity, and the implementation cost in practical engineering.

In my opinion, the best controller in general, should have the robust adaptive feature.

Good luck!

Depend on your system and your target. PI is very simple and easy.

Which is the "best" controller? This depends from:

1. dynamics of controlled process.

2. demanded cotrol loop quality.

The "best" controller for proportional second order controlled proces and demanded loop dynamics as  proportional I. order, is PID controller. This can be very simple explain in mathematics area. 

But.... This is the thruth only for the continuos linear systems. Every output of controller has the "restriction" (limitation). Than you have to use ARW -Anti Reset WindUp, which is very good described for the discrete time area. Also some modification, which respect the "sampling interval" of discrete controller it is usefull.

From my point of wiew the "best" controller is the "state controller, together with state estimator" with synthesis for "modal state controller".

For servomechanism is the "best controller" the time optimal controller or energy optimal controller, which can be exactly (with respect the controller limitation) described for II. order proportional controlled systems. For controlled systems with more complex dynamics (as servomechanism) is better to use "sliding mode controller".

In this time we known also "adaptive cpntrollers" (with continuos identification or without ideentification). For control processes with dynamics bigger than "second order" , you can use "adaptive controller without identification".

For the special controlled processes it can be use 2 or 3 controllers, when there is one  main feedback and auxiliary feedbacks with failure "model" etc.

A special case is when in the "closed loop" is "model of the control loop" etc.

So the question "Is PI controller still the best controller up till now?" is the question from the 1960 year, and "now" this question has no justification.

The selection of controller is done via various ways:

1. Desired closed loop performances

2. Type of a plant to be controlled.

3. Robustness of the system.

4. Type of system uncertainties etc.

There is nothing like that PI is better or PIDA is better controller. Depending on the requirements of the system to be controlled, the controllers are designed and then the comparative analysis is performed to analyze the closed loop performances to verify which one is better. 

It is just that the PID class of controllers are oldest and simplest controllers and can be practically implementable easily. Otherwise, there are various controllers in literature that can be utilized instead of PI/PID/PIDA for specific plants and give much better performances.

Hi,

ADRC that is taking off as a technology after numerous successful applications in engineering. 

The ADRC solution was recently deployed at a Parker Hannifin Extrusion Plant in North America, resulting in over 50% energy saving per line across ten production lines, together with significant improvements in product quality.  Also, Kinetis® motor suite reduces field oriented control (FOC) motor control design time cycle with its simple to use interface and design methodology, increases system performance, and reduces support costs with Active Disturbance Rejections Control (ADRC) . It supports three-phase BLDC and PMSM motors via algorithm with either low-cost sensorless or high-accuracy sensored control implementations. Texas Instrument has adopted the ADRC technology in developing and distributing a new line of motion control chips (InstaSPIN™-MOTION) worldwide. Furthermore, an implementation of ADRC is available in the LineStream Technologies, SpinTAC Motion Control Suite. SpinTAC is featured on Texas Instruments’ microcontrollers (MCUs) with InstaSPIN-MOTION technology. The National Superconducting Cyclotron Lab in the U.S. has implemented ADRC in several high energy particle accelerators after significant improvements have been obtained in amplitude and phase regulation of electromagnetic fields.

Thank you all. I totally appreciate your help. your answers are of a great benefit for my research

Please refer to this article:

https://www.researchgate.net/publication/318726178_An_Improved_Active_Disturbance_Rejection_Control_for_a_Differential_Drive_Mobile_Robot_with_Mismatched_Disturbances_and_Uncertainties

Conference Paper An Improved Active Disturbance Rejection Control for a Diffe...

Is PI the best controller ? My answer is no PI is a common simple control, SLIDE MODE CONTROL is more robust as compared to PI.

Although, PI has its own limitations which may not be applicable to all of systems. However, for the following reasons PI or PI-based (PI+ harmonic filters) are good choice at least for the switching power systems:

1- Less computation burden in the simulation process. Complicated controllers simulation time is quiet high.

2- Easily applicable in practice. Nonlinear controllers need high switching frequency while PI switching frequency can be selected low. Most of micro-controllers and dSPACES have switching limitations.

3- Easy design process.

PI is not the best controller but generally easy and sufficient if your system is simple.

Most classical controllers have overshoot at the start including PI controller, but one of the variant of Sliding mode controller called Super twisting SMC have a more robust response which also have no overshoot at the start, also have lesser steady state error as compared to PI controller.

You can read my recent publication about comparison between classical and SMC.

4- The PI (or Cascaded-PI) shows low pass filter behavior which can reduce current chattering, then it is good for switching systems.

The answer to your question totally depends on the type of system you are using. Im also working on a similar thing, Im trying to compare a Self tuning Controller and the PI controller in a Grid connected inverter.