Quantitative analyses of robust stability region and disturbance response of processes with an integrator and long dead-time

Different control schemes for processes with an integrator and long dead-time have resulted in the same disturbance response. Moreover, it has already been shown that such a response is sub-ideal. Hence, it is quite necessary to quantitatively study the achievable specifications and robust stability region. This paper is devoted to do so. As a result, the control parameter is able to be chosen with compromise between disturbance response and robustness quantitatively. Four specifications-(normalized) maximum dynamic error, maximum decay rate, (normalized) control action bound, and approximate recovery time-are given to measure the response of step disturbance. It is pointed out that any attempt to get normalized dynamic error less than τ_m is impossible and the allowable bound of relative gain uncertainty is √(3/2)