This paper addresses an on-off damping tuned liquid column damper (TLCD) regulated by a general controller. This general controller can represent many conventional controllers such as groundhook, skyhook, bang-bang, or linear clipping controller. Due to the on-off damping and quadratic damping of the TLCD the system is complex nonlinear. To cope with those nonlinearities, this paper presents a simple approximated solution by solving a scalar algebraic equation. Outcomes of numerical simulations verify the proposed approximated solution. Moreover, the approximated solution is useful to clarify the condition of robust controllers, to speed up the optimization of the general controller, and to conduct any parametric study. Based on a parametric study, an empirical formula for the optimized parameters of the general on-off damping controller is derived. In a case study of an earthquake excited five degree-of-freedom shear frame the simplicity, robustness, and effectiveness of the semi-active TLCD with optimized parameters is illustrated, considering limited noisy measurements, time delay, modeling error, and nonlinear TLCD behavior.