Optimal digital controllers for double integrator: comparison of four methods

Four methods for the design of optimal digital controllers for the double integrator are compared including: discretization of the optimal continuous-time controller, discrete-time design of proper and strictly proper optimal controllers, and direct sampled-data design. Algorithms under investigation are realized with the robust control toolbox, and the DirectSD toolbox for MATLAB. It is shown that all approximative design methods lead to unacceptable system performance in continuous time. An important conclusion is that the situation is not improved even if one decreases the sampling period. Moreover, for small sampling periods the amplitude of the control signal increases significantly.