An ultrasonic surgical system comprising: a transducer; an end effector coupled to the transducer and configured to grasp and seal a vessel; a power source (110, 210) configured to supply electrical energy for the transducer; a sensor configured to sense parameters of the vessel for estimating a size of the vessel; and a controller configured to: estimate a size of the vessel based on the sensed parameters; control the electrical energy based on maintaining a predetermined initial heating rate of heating the vessel until a predetermined amount of energy corresponding to the estimated size of the vessel has been delivered; and control the electrical energy based on a predetermined heating rate curve of heating the vessel after the predetermined amount of energy corresponding to the estimated size of the vessel has been delivered, characterized in that: the controller is configured, in controlling the electrical energy based on maintaining the predetermined initial heating rate of heating the vessel, to control an amplitude of the electrical energy based on the detected rate of change of a resonant frequency of the transducer over time; and the controller is configured, in controlling the electrical energy based on the predetermined heating rate curve of heating the vessel, to: detect a rate of change of a resonant frequency of the transducer over time, and control an amplitude of the electrical energy based on the detected rate of change of the resonant frequency over time. a transducer; an end effector coupled to the transducer and configured to grasp and seal a vessel; a power source (110, 210) configured to supply electrical energy for the transducer; a sensor configured to sense parameters of the vessel for estimating a size of the vessel; and a controller configured to: estimate a size of the vessel based on the sensed parameters; control the electrical energy based on maintaining a predetermined initial heating rate of heating the vessel until a predetermined amount of energy corresponding to the estimated size of the vessel has been delivered; and control the electrical energy based on a predetermined heating rate curve of heating the vessel after the predetermined amount of energy corresponding to the estimated size of the vessel has been delivered, characterized in that: the controller is configured, in controlling the electrical energy based on maintaining the predetermined initial heating rate of heating the vessel, to control an amplitude of the electrical energy based on the detected rate of change of a resonant frequency of the transducer over time; and the controller is configured, in controlling the electrical energy based on the predetermined heating rate curve of heating the vessel, to: detect a rate of change of a resonant frequency of the transducer over time, and control an amplitude of the electrical energy based on the detected rate of change of the resonant frequency over time. estimate a size of the vessel based on the sensed parameters; control the electrical energy based on maintaining a predetermined initial heating rate of heating the vessel until a predetermined amount of energy corresponding to the estimated size of the vessel has been delivered; and control the electrical energy based on a predetermined heating rate curve of heating the vessel after the predetermined amount of energy corresponding to the estimated size of the vessel has been delivered, characterized in that: the controller is configured, in controlling the electrical energy based on maintaining the predetermined initial heating rate of heating the vessel, to control an amplitude of the electrical energy based on the detected rate of change of a resonant frequency of the transducer over time; and the controller is configured, in controlling the electrical energy based on the predetermined heating rate curve of heating the vessel, to: detect a rate of change of a resonant frequency of the transducer over time, and control an amplitude of the electrical energy based on the detected rate of change of the resonant frequency over time. the controller is configured, in controlling the electrical energy based on maintaining the predetermined initial heating rate of heating the vessel, to control an amplitude of the electrical energy based on the detected rate of change of a resonant frequency of the transducer over time; and the controller is configured, in controlling the electrical energy based on the predetermined heating rate curve of heating the vessel, to: detect a rate of change of a resonant frequency of the transducer over time, and control an amplitude of the electrical energy based on the detected rate of change of the resonant frequency over time. detect a rate of change of a resonant frequency of the transducer over time, and control an amplitude of the electrical energy based on the detected rate of change of the resonant frequency over time.