By Gang Tao PhD, Shuhao Chen, Xidong Tang, Suresh M. Joshi PhD (auth.)
When an actuator fails, chaos or calamity can frequently ensue.
It is as the actuator is the ultimate step within the keep watch over chain, while the regulate system’s directions are made bodily genuine that failure could be so very important and tough to make amends for. whilst the character or place of the failure is unknown, the offsetting of consequent approach uncertainties turns into much more awkward.
Adaptive keep an eye on of platforms with Actuator Failures facilities on counteracting occasions during which unknown keep an eye on inputs turn into indeterminately unresponsive over an doubtful time period through adapting the responses of closing sensible actuators. either "lock-in-place" and varying-value mess ups are handled. the consequences offered demonstrate:
• the lifestyles of nominal plant-model matching controller constructions with linked matching stipulations for all attainable failure patterns;
• the alternative of a fascinating adaptive controller structure;
• derivation of novel mistakes versions within the presence of failures;
• the layout of adaptive legislation permitting controllers to reply to combos of uncertainties stemming from activator mess ups and process parameters.
Adaptive keep watch over of platforms with Actuator Failures could be of value to manage engineers usually and particularly to either lecturers and commercial practitioners engaged on safety-critical platforms or these during which full-blown fault id and analysis is both too time eating or too expensive.
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Additional info for Adaptive Control of Systems with Actuator Failures
M0 , the 22 Chapter 2 State Feedback Designs for State Tracking ∗ ∗ unknown plant-model matching parameters K1∗ , k2∗ , and k3∗ (that is, k1j , k2j , ∗ k3j , j = 1, . . 28) for j = 1, . . , m, i = 0, 1, . . , m0 . Suppose there are p failed actuators, that is, uj (t) = u ¯j , j = j1 , . . , jp , 1 ≤ p ≤ m − 1, at time t ∈ (Ti , Ti+1 ) (with i = i(p) ≤ p because there may be more than one actuator failing at the same time Ti ). ,jp = AM x(t) + bM r(t) + bM 1 k˜T (t)x(t) + k˜2j (t)r(t) + k˜3j (t) .
1. 163) where Ba ∈ Rn×(m−p) consists of m − p columns of B, bj , j = j1 , . . , jp . 159). Since Ba consists of only bj , j = j1 , . . , jp , rank(Ba ) < rank(B) means that there is at least one of bj , j = j1 , . . , a column of Bf ), that cannot be expressed as a linear combination of the columns of Ba . Since u ¯j , j = j1 , . . 160). 160). 163) means rank(Ba ) = rank([Ba |Bf u ¯f ]). 160). 165) ∇ Plant-Model Matching with up to m − q Actuator Failures. Now we consider the case of up to m − q actuator failures.
117). ∗ ∗ ∗ ∗ ∗ ∗ , k11j , k21i , k22j , k31i , and k32j , i = i1 , i2 , . . , ip1 , j = The choice of k11i j1 , j2 , . . , jp2 , is irrelevant because their actuators have failed. 134) where the controller parameters K1 = [k111 , . . , k11m1 , k121 , . . , k12m2 ] ∈ Rn×m K2 = k211 , . . , k21m1 , 0, . . , 0 0, . . , 0, k221 , . . , k22m2 T ∈ Rm×2 k = [k311 , . . , k31m1 , k321 , . . 135) are the estimates of K1∗ , K2∗ , and k3∗ , respectively. 1m) sign[ks21i ] and sign[ks22j ], i = 1, .