This paper presents new linear-quadratic-regulator-based multivariable PID controller design conditions for MIMO uncertain second-order systems. The gain matrices of the multivariable PID controller are computed by solving an LMI problem which minimizes a cost function consisting of the expectation of the sum of quadratic forms relating the system states and control effort. The linear-quadratic-regulator-based design is much more intuitive to tuning than the eigenvalue assignment within a desired set or region for placement, in which a balance between the state trajectories and control energy is pursued through the tuning parameters. The proposed design methodology was tested on an experimental platform consisting of a mobile inverted pendulum robot, an underactuated and challenging control problem to ensure stability and performance. The obtained results support the theoretical findings.
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