Experimental Validation of a Numerical Controller Using Convex Optimization with Linear Matrix Inequalities on a Quarter-Car Suspension System
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Numerical methods of designing control systems are currently an active area of research. Convex optimization with linear matrix inequalities (LMIs) is one such method. Control objectives like minimizing the H_2, H_infinity norms, limiting the actuating effort to avoid saturation, pole-placement constraints etc., are cast as LMIs and an optimal feedback controller is found by making use of efficient interior-point algorithms. A full-state feedback controller is designed and implemented in this thesis using this method which then forms the basis for designing a static output feedback (SOF) controller. A profile was generated that relates the change in the SOF control gain matrix required to keep the same value of the generalized H_2 norm of the transfer function from the road disturbance to the actuating effort with the change in the sprung mass of the quarter-car system. The quarter-car system makes use of a linear brushless permanent magnet motor (LBPMM) as an actuator, a linear variable differential transformer (LVDT) and two accelerometers as sensors for feedback control and forms a platform to test these control methodologies. For the full-state feedback controller a performance measure (H_2 norm of the transfer function from road disturbance to sprung mass acceleration) of 2.166*10^3 m/s^2 was achieved ensuring that actuator saturation did not occur and that all poles had a minimum damping ratio of 0.2. The SOF controller achieved a performance measure of 1.707*10^3 m/s^2 ensuring that actuator saturation does not occur. Experimental and simulation results are provided which demonstrate the effectiveness of the SOF controller for various values of the sprung mass. A reduction in the peak-to-peak velocity by 73 percent, 72 percent, and 71 percent was achieved for a sprung mass of 2.4 kg, 2.8 kg, and 3.4 kg, respectively. For the same values of the sprung mass, a modified lead-lag compensator achieved a reduction of 79 percent, 77 percent and, 69 percent, respectively. A reduction of 76 percent and 54 percent in the peak-to-peak velocity was achieved for a sprung mass of 6.0 kg in simulation by the SOF controller and the modified lead-lag compensator, respectively. The gain of the modified lead-lag compensator needs to be recomputed in order to achieve a similar attenuation as that of the SOF controller when the value of the sprung mass is changed. For a sprung mass of 3.4 kg and a suspension spring stiffness of 1640 N/m the peak-to-peak velocity of the sprung mass was attenuated by 42 percent.