The use of a demand response controller is necessary for electric devices to effectively respond to time varying price signals and to achieve the benefits of cost reduction. This paper describes a new formulation with the form of constrained optimization for designing an optimal demand response controller. It is demonstrated that constrained optimization is a better approach for the demand response controller, in terms of the ambiguity of device operation and the practicality of implementation of the optimal control law. This paper also proposes a design scheme to construct a demand response controller that is useful when a system controller is already adapted or optimized for the system. The design separates the demand response function from the original system control function while leaving the system control law unchanged. The proposed formulation is simulated and compared to the system with simple dynamics. The effects of the constraints, the system characteristics and the electricity price are examined further.