I need to choose from these 3 controllers the best one.

what I found in my new researches about TSMC is :

Compared with linear hyper-plane based sliding modes, TSM offers some superior properties such as fast, finite time convergence. This controller is particularly useful for high precision control as it speeds up the rate of convergence near the equilibrium point, which has been used for second or high nonlinear uncertain systems control. However, just like general sliding mode control, the chattering phenomenon caused by discontinuous control signal (a general problem associated with SMC control) is not addressed sufficiently.

A novel dynamic terminal sliding mode control eliminates the chattering problem by using dynamic terminal sliding mode surface. By using a function augmented sliding hyper-plane, it is guaranteed that the tracking error converges to zero in finite time. In addition, the reaching phase problem is totally eliminated whenever an initial state is located in the phase space. Therefore, the overall system is always in the sliding mode and shows the invariance property to parameter variations during the entire response time.

this is from the article:

A novel dynamic terminal sliding mode control of uncertain nonlinear systems

Higher order SMC:

It can elliminate chattering thoroughly and converges in finite time with more accuracy than SMC.

Also , it is useful for the system with complicated model , like robotic manipulator , as it does not depend on the model.

TSM is a precision based control. If implemented right, it can achieve fast convergence and finite-time convergence. However, it typically suffers from the flaw that the control is not smooth and could become singular/unbounded, at times. Unless a non-singular sliding surface is adopted. Like x_1+x_2^(1/a)=0 instead of x_1^a+x_2=0

On the contrary, the aim of HOSM is smoothening of the system response. Hence, the control and the response can be made more smooth and finite. It is a robust technique, therefore precise control is not guaranteed per se. It guarantees that the evolution of the sliding function and its derivatives are smooth,

Application of HOSM on a power-rate sliding surface (TSM), for systems with uncertainty would lead to finite convergence to within a boundary in the neighbourhood of origin.

Based on the metrics of assessment, it is for the user to choose which is best.