You can try controller design methods such as H-infinity or H2 synthesis that are more robust and can reject disturbances more effectively.

Here some good references to understand that 2 DoF PID controllers are easy to design and tune:

Chapter Optimum PI/PID Controllers Tuning via an Evolutionary Algorithm

Chapter Two-Degree-of-Freedom PID Controllers Structures

Article Simple Robust Tuning of 2DoF PID Controllers From A Performa...

The main advantage of 2DoF controllers is their capability to do both at the same time: track references and reject disturbances. Time delay is not a requirement or limitation.

Dear Malyala Venkata Satya Sai Chandra

Although at the first glance, it seems an elementary text-book in control engineering, whereas, I think the text-book introduces the most fundamental concepts of control engineering through an intuitive illustration, which could concomitantly give a better understanding of the most advanced control topics. Although the text-book seems naïve, whereas, if you get deeper in its sentences, some very advanced concepts could be easily revealed.

I mean the book: Modern Control Engineering, by Katsuhiko Ogata .

Notice, the attachment, please.

Dear Chandra,

If you can write an appropriate objective function. You can adjust and tune Cascade PID parameters with lots of metaheuristic algorithms. I can recommend you to examine the following studies. Best. Hasan.

Article Tuning of LQR controller for an experimental inverted pendul...

Article ÇİFT TERS SARKAÇ SİSTEMİNİN DENGE VE KONUM KONTROLÜ İÇİN ARI...