This paper will first describe the Linear-Quadratic-Gaussian (LQG) and Lead-Compensator when the Proportional-Integral-Derivative (PID) controllers are inactive for procedures that have large delay time (LDT) in transfer stage. Therefore in those states, LQG and Lead Compensator perform better than the PID controllers. The constrained LQG is optimal and stabilizing. The solution algorithm is guaranteed to terminate in finite time with a computational cost that has a reasonable upper bound compared to the minimal cost for computing the optimal solution. In this work all actual working area condition for instance noises and disturbances are considered. Eventually, LQG and Lead Compensator have been designed for a thermal system, which circulates hot air to keep the temperature of a chamber constant and finally the results are analyzed and compared.
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