This paper investigates the use of a linear time-invariant (LTI) control framework to optimally design multiple tuned mass dampers (TMDs) that minimize unwanted vibrations caused by exogenous disturbance forces to a ram-type structure with varying dynamic characteristics. A key challenge for the development of the LTI control framework is the reformulation of the TMDs’ design parameters, which consist of linear and nonlinear parameters as static feedback gains. This paper proposes the use of extra cascade control inputs to reformulate the optimization problem into an LTI control framework for the simultaneous optimization of linear (i.e., stiffness and damping) and nonlinear (i.e., location) parameters. A rigid planar system with multiple attached TMDs is developed as a mathematical model. It is reconstituted as an LTI framework by connecting a control input for the location parameter with control inputs for the stiffness and damping parameters. The model is then optimized using multi-model H∞ synthesis. A commercial gantry-type machining center is used to validate the proposed approach. Results from the simulation and experiment show that the optimized multiple TMDs systematically designed by this approach improve the system's dynamic stiffness by up to 83% and increase the allowable maximum depth of cut from 1 mm to 1.5 mm.