When active noise control (ANC) systems are actually implemented, it is necessary to take account of the modeling error of an error path. The modeling error limits the performance of ANC and it makes the system unstable at worst. The characteristics of the error path cannot be assumed to be stable, so that on-line estimation is preferred for actual applications such as an active control system of the exhaust noise of an engine. An adaptive algorithm called the delayed-X harmonics synthesizer (DXHS) algorithm for periodic noise has been proposed. This algorithm controls amplitude and phase parameters for each harmonic component. The original algorithm controls parameters represented in polar coordinates with constant delay parameters. This paper presents an extended algorithm to estimate delay parameters of the error path on-line. Delay parameters, which are important for the stability, are introduced as a phase, while other parameters are represented in orthogonal coordinates. The performance of the algorithm is evaluated by computer simulations. When SNR at the control point is 0 dB, the estimate delay is nearly the same value as the actual delay, and the system converges very stably.