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For this reason, there is a potential risk that this exchange operate is just not add up to 3 once the change will be MRIP done in between constant transmission and also digital camera signs. Although it might be little, it has damaging relation to the sturdy efficiency in the event the height and width of Mi�� is very large ample, the 2nd key reason to perform some pretreatment recommended in Part 3.A couple of. 4.A couple of. Your Indicator FD Based on Associate States As a way to implement the sensor FD associated with express xi, x?i can be be defined as the actual associate express. Assume it could be tested by the sensing unit as well as x?�Bi=xi . Combining x?�Bi=xi as well as (12), we: {[x?�Bi?xi]=[010a][x?ixi]+[0b]ul+[01]d[y1y2]+[x?ixi]+[f?sfs] (26) where f?s denotes the sensor fault of x?i. Then (26) can be rewritten by: {x?=Ax+Bul+Edy=Cx+f (27) where A=[010a] , B=[0b] , C=[1001] check details , E=[01] , x=[x?ixi] , f=[f?sfs] Subsequently, the following result exists. Theory 5: the perfect decoupling, discussed in Section 3, comes true by the assistant state in (27). Proof: According to Lemma 1, the proof is straightforward. Depending on the above discussion, the observer (24) can be used to generate the residual, namely: {x^�B=Ax+Bul+K(y?y^)y^=Cx^ (28) So, the residual (25) is obtained, i.e.: r(s)=W(y?y^)Grdd+Grff (29) Theory 6: when W=[10] K=[��110a+��2] , the model uncertainty, actuator fault and disturbance in (29) will be decoupled from the residual in (25) perfectly. ��1 and ��2 are two positive real numbers. Proof: According to lemma 1, when W=[10] K=[��110a+��2], it exists Grd = 0. So: r(s)=W(y?y^)=ss+��1f^s?1s+��1fs (30) So, the inverse Laplace transformed residual in (25) is: r(t)=e?��1tf?s?1��1(1?e?��1t)f^s (31) Then, the fault is detected successfully described by: limt����r(t)=?1��1fs (32) From the steady state value of the residual in (32), the information of the target sensor fault is presented intuitively. The size and type of sensor fault could be achieved easily through combining the residual in (32) and the typical mathematical feature of sensor fault. Remark 10: when the input from the controller couldn't be achieved, the input of the observer is 0. The sensor FD approach provided in this section is still valid. www.selleckchem.com/products/Temsirolimus.html It has no influence on the sensor FD whether the input of the controller in observer (24) exists. The only influence is on the model uncertainty. The feature will make the approach be widely used in the large complex plant. 4.3. The Existence of the Assistant State The integral of state xi is sure to exist, which is the assistant state x?i. When it couldn't be measured by a sensor, the analytical relationship and the measurements from other sensors in the plant could be used to calculate the value of x?i.