We address analysis and design problems of aggregate demand response systems composed of various consumers based on controllability to facilitate to design automated demand response machines that are installed into consumers to automatically respond to electricity price changes. To this end, we introduce a controllability index that expresses the worst-case error between the expected total electricity consumption and the electricity supply when the best electricity price is chosen. The analysis problem using the index considers how to maximize the controllability of the whole consumer group when the consumption characteristic of each consumer is not fixed. In contrast, the design problem considers the whole consumer group when the consumption characteristics of a part of the group are fixed. By solving the analysis problem, we first clarify how the controllability, average consumption characteristics of all consumers, and the number of selectable electricity prices are related. In particular, the minimum value of the controllability index is determined by the number of selectable electricity prices. Next, we prove that the design problem can be solved by a simple linear optimization. Numerical experiments demonstrate that our results are able to increase the controllability of the overall consumer group.