Optimal solution of equation (10) without switching. The optimum parameters are: α_opt = 0.22 and β_opt = 0.83. a) Left vertical axis: dimensionless motion of the electrode z(t) (blue solid line) and charge q(t) (green dot-dash line). Right vertical axis: voltage u(t) (thick red dashed line). b) U-Q cycle in dimensionless variables, showing efficiency of 25.4%, calculated in the steady state regime.