In general, it is hard to check exhaustively states of systems that behave continuously over time and space, unlike the systems with discrete state space. Therefore, falsification methods of temporal logic formulae have been proposed as a prominent approach to verify various continuous systems. The falsification methods efficiently compute a counterexample of continuous systems that does not satisfy a considered property based on the numerical simulation and statistical optimization. In this research, we consider continuous systems that involve controllers, and aim for a simple description of controller specifications and the automated tuning of controller parameters based on the quantitative evaluation of the specification. To achieve this goal, we encode the specifications as temporal logic formulae, formalize an optimization problem about the parameters, and propose an algorithm that solves this optimization problem with a statistical method. The proposed method enables to describe various controller specifications, to evaluate the specifications quantitatively, and to optimize parameters efficiently for the generic controllers. We experimentally tuned PID controllers connected with typical physical systems, and confirmed that our method computed quantitatively better parameter configurations than the classical Ziegler-Nichols method.