Discrete LQ suboptimal control of cable suspended loads

In this paper we consider the problem of controlling the position of a cable suspended mass and design the optimal controller according to a quadratic cost index. Since in industrial applications it is a common practice to apply digital controllers, we perform the controller design and stability analysis in discrete-time domain. The optimization problem is solved analytically which guarantees that the obtained control law is simple in implementation. We discuss parameter selection so that the mass acceleration is constrained to a prescribed range. Moreover, since in certain applications (such as lifts) overshoots and oscillations of the position should be avoided, we define conditions for eliminating undesirable fluctuations of the output variable.