Design of a stable state feedback controller based on the multirate sampling of the plant output.

*(English)*Zbl 0648.93043It is generally recognized that controllers should have the following properties:

(1) controllers themselves are stable,

(2) controllers can execute any pole assignment,

(3) controllers do not cause rapid change of input signals,

(4) computational effort to construct controllers is not so heavy.

After examining past researcher in this field, the authors conclude that introduction of periodically time-varying elements into controllers will bring about improvement of controller ability. Multirate-output controllers (MROC) are proposed in this paper. MROC changes the plant input once in a frame period \(T_ 0\), while detecting its output \(N_ i\) times during \(T_ 0\). Control inputs are determined by the rule \(u((k+1)T_ 0)+M(kT_ 0)-H\hat y(kT_ 0)\) where M is the state transition matrix of the controller and \(\hat y(kT_ 0)\) is a \(\sum^{p}_{i+1}N_ i\) dimensional vector. Theorem 1 shows that this scheme is equivalent to any state variable feedback. Theorem 2 shows that M can be chosen arbitrarily for any state variable feedback law, and hence it is concluded that stable controllers can always be implemented. The authors say that since MROC satisfies the equired conditions for the controllers, it is very suitable for use as industrial process controllers.

(1) controllers themselves are stable,

(2) controllers can execute any pole assignment,

(3) controllers do not cause rapid change of input signals,

(4) computational effort to construct controllers is not so heavy.

After examining past researcher in this field, the authors conclude that introduction of periodically time-varying elements into controllers will bring about improvement of controller ability. Multirate-output controllers (MROC) are proposed in this paper. MROC changes the plant input once in a frame period \(T_ 0\), while detecting its output \(N_ i\) times during \(T_ 0\). Control inputs are determined by the rule \(u((k+1)T_ 0)+M(kT_ 0)-H\hat y(kT_ 0)\) where M is the state transition matrix of the controller and \(\hat y(kT_ 0)\) is a \(\sum^{p}_{i+1}N_ i\) dimensional vector. Theorem 1 shows that this scheme is equivalent to any state variable feedback. Theorem 2 shows that M can be chosen arbitrarily for any state variable feedback law, and hence it is concluded that stable controllers can always be implemented. The authors say that since MROC satisfies the equired conditions for the controllers, it is very suitable for use as industrial process controllers.

Reviewer: K.Ichikawa