Professor of Control Engineering
Department of Electronic and Control Systems Engineering
Interdisciplinary Faculty of Science and Engineering
1060 Nishikawatsu-cho, Matsue 690-8504, JAPAN
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A design method of a controller with a variable feedback gain is presented for a linear sampled-data plant subject to a control constraint. The performance index considered here is a quadratic function of the state. A set of the steady state LQ optimal gains and their associated linear regions, i.e., the sets of initial conditions such that the control via the gain satisfies the constraint, are utilized to determine the control signal. The resulting control law is a state feedback via the state-dependent piecewise constant feedback gain which becomes progressively higher as the state approaches the equilibrium point. The closed loop system is more effective than the steady state LQ optimal regulator which satisfies the constraint. Calculations for obtaining the control signal are relatively simple as compared with perfect optimal control.
It is also shown that the linear region can be described by a set of inequalities. A few examples of simulation experiments are also presented.
Key Words - Maximal set of admissible initial states (Maximal output admissible set), system design, variable gain, bounded control, quadratic cost.
The mechanical energy of a pendulum whose pivot can move horizontally can be controlled according to signs of the pivot acceleration values. A servo design technique is proposed which can control the pivot acceleration considering a limited travel of the pivot. This control law is applied to the swing-up control problem for an inverted pendulum.
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