A universal single-input-single-output (SISO) controller is proposed which is based on higher-order sliding modes and requires output measurements only. The uncertain SISO dynamic system to be controlled is required to have a permanent known-in-advance relative degree. Its exact mathematical model is not needed. The proposed controller provides for exact finite-time-convergent output tracking with exact output measurements, otherwise the tracking accuracy is proportional to the magnitude of the measurement noise. The control may be made arbitrarily smooth, thereby removing the chattering effect.