A plant controller controls a plant modeled in a discrete-time system. The controller uses a frequency-shaping response-designating control algorithm having a filtering function to cause a difference between output of the plant and a target value to converge. Thus, the plant is robustly controlled without causing undesired frequency components. When the plant is an engine, the engine is modeled using a ignition timing corrective quantity as input and a rotational speed as output. The controller performs the frequency-shaping response-designating control algorithm to determine the ignition timing corrective quantity. The frequency-shaping response-designating control may be frequency-shaping sliding-mode control. In one embodiment, the control input into the plant may includes a corrective term for stabilizing an internal variable of the filter, a corrective term for stabilizing the difference between the output of the plant and the target value and a corrective term that varies depending on a switching function.