It is well known that undershoot phenomena are inevitable for plants having real unstable zeros. This book, firstly investigate the undershoot phenomena caused by unstable zeros of the plant to be controlled theoretically. Then, propose methods of reducing the undershoot amount for a plant with unstable zeros by digital control. The ideas are based on the Linear Quadratic Regulator (LQR) design is to use a modified performance index with an exponential time decay rate using a weighting factor and confirm from simulation results that the weighted optimal LQR can reduce undershoot in comparison with the standard LQR case.?The next method to reducing the undershoot amount is by using digital control design. The idea here is a combination of the discrete version of the weighted optimal LQR and a discrete-time controller design with Piecewise Constant Hold (PCH) instead of Zero Order Hold (ZOH). By using PCH can change the inter-sample control input so as to reduce the undershoot amount. The effectiveness of all method have evaluated by dynamical system.

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