Is there any other controller than PID Controller? I have been given a Project to search for a controller having better transient response than PID Controller. I searched but I didn't find any research paper on it. All are talking about improving PID's transient response but I am unable to find any other Controller with the better transient Response. Can anyone share comparative analysis between the aforementioned controllers Or a Research Paper? Or can someone list controllers?
P.S: I'm new in Control Theory field.
 A: Of course there are other controllers than PID... there's a reason for the large amount of ongoing work in Control Theory at research universities.
Perhaps the next level up in terms of sophistication from PID is the Linear Quadratic Regulator (LQR). LQR control uses a linear state-space model of the system. The basic idea is that you define a convex quadratic cost function, which encodes which inputs/actuators and states you care about most. The cost function penalizes the use of the inputs and also penalizes the deviation of the states from your desired setpoint. For your example, since you care mostly about transient response, you would probably heavily weight the state variables associated with signal you care about (for instance, position or voltage), as well as the derivative of that signal (which is typically taken as a state variable for second- and higher-order systems). With your cost function defined, you then minimize the cost with respect to the control input. LQR is particularly remarkable since the optimal control input ends up being a time-invariant linear state feedback of the form $u(t) = Kx(t)$, where $K$ solves the algebraic Ricatti equation. LQR is also powerful because it naturally encodes various robustness properties into the closed-loop system.
Another level up in sophistication is model predictive control. Model predictive control (MPC) can be thought of as online optimal control, i.e., solve LQR (or a finite-time optimal control problem) at each time step, then send the first time step of the optimal control input to the system, then repeat the process at the next time step. MPC performs particularly well on systems whose dynamics include slight unmodeled dynamics or unmodeled disturbances, since the act of re-solving the optimal control problem at each time step acts as a feedback mechanism to take the effects of these unmodeled behaviors into account.
More recently, there has been a lot of work in the research community where data-driven methods from machine learning are being used in conjunction with model-based control strategies in order to achieve certain control goals.
The bottom line is, yes, there is an entire literature on more sophisticated control methods than PID, and this body of work is growing by the day now that the fields of machine learning, control theory, and optimization are finding novel intersections. A great new conference in this area is L4DC (Learning for Dynamics and Control). I suggest you take a look at this year's papers to get an idea of what is going on in the field. Two other staple conferences for the control theory community are CDC (Conference on Decision and Control) and ACC (American Control Conference).
I hope this helps give you some new directions!
