Robust tilt‐integral‐derivative controller synthesis for first‐order plus time delay and higher‐order systems

ABSTRACT A tilt integrator of the tilt‐integral‐derivative (TID) controller is an integrator to the power of a fraction. The current state of the art of TID controller is difficult to satisfy prespecified frequency‐domain specifications and is not able to build the connection between the frequency‐domain synthesis and time‐domain analysis. To fill the gap in TID control theory, a systematic tuning method of robust TID controller for first order plus time delay (FOPTD) and higher‐order processes is proposed, which is based on combining frequency‐ and time‐domain specifications synthesis. The TID controller parameters , , and optimal fractional order are settled to meet frequency‐domain specifications including phase margin, gain crossover frequency, and flat phase constraint that guarantee systemic stability and robustness. The parameter can be determined under the time‐domain specification including the smallest ITAE that achieves optimal dynamic performance. In addition, the steps of the proposed robust TID controller design process are given in detail, and an example is given to illustrate the corresponding steps. At last, the control and gain variation performances of the obtained TID controller are compared with some other controllers (PID, FOPI, and FOPID). Simulation results for FOPTD and higher‐order systems illustrate the superior robustness as well as the transient performance of the proposed control tuning procedure. To verify the practical usefulness of the outcomes of this paper, some experimental results on temperature control of a Peltier cell are presented.