New criteria for the existence of a switching controller for output signal shaping

Although numerous advanced and intelligent controllers have been invented during the last years, classical PID controllers are still of interest to many control engineers and promising candidates for industrial purposes. In this study, the authors study the issue of when a switching controller gains exist to asymptotically track a predefined output profile for secondorder linear timeinvariant systems. This paper proposes several new criteria to ascertain the existence of the gains of PID controllers so that the output be in predefined values at special times. Since permitted output range is calculated for the nonzero initial values, we can switch between several PID gains in several steps to have a specific variation of output with time. In this way, several desired targets can be achieved without any compromising. It is the main goal of this paper. In fact, a scenario is considered for the output which determines its values in several times and these times generate time intervals over which variable gains are applied to the system. Requirements for tracking can be readily achieved with choosing the output value according to the criteria. It is evaluated by several simulation examples, which demonstrate that the proposed approach works well to obtain PID controller parameters in a guaranteed way.