A new dual pole-placement controller (APPC), and a dual linear quadratic Gaussian (LQG) controller with indirect adaptation are designed and applied to the speed control of a thyristor-driven direct-current (DC) motor. The suggested synthesis approach is based on bi-criterial optimisation of two cost functions, introduced to give the adaptive controllers properties of caution and allow them to stimulate the parameter estimation. The derived controllers are computationally simple, and the standard APPC and the LQG controller based on the certainty equivalence (CE) assumption, can easily be modified in their dual versions by generating the cautious part of the control signal and then adding the stimulating part. The derived LQG controller is obtained using spectral factorisation and pole positioning, which corresponds to the optimum cost function of the LQG controller. The designed controllers are applied to the speed control of a thyristor-driven DC-motor. The described experimental application demonstrates the superiority of the designed controllers over the standard APPC, and the LQG controller based on the CE approach.