- Question 3 17 Marks Consider A Control System Described By The Following State Variable Model X T Ax T Bu T Y T 1 (139.82 KiB) Viewed 13 times
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Question 3 (17 marks) Consider a control system described by the following state variable model x(t)- Ax(t) + Bu(t) y(t) = Cx(t) + Du(t) with A »^=[RJ]®=* *]=[ }) and D = [*] (a) Determine the dimension of the input u(t) and output y(t) respectively and obtain the characteristic equation of the system. [4 marks] (b) Find the state-transition matrix for k₁ = 1 and k₂ = 1. [5 marks] (c) For system in (b), assume the initial condition is x(0)-[¹] determine the unforced time response (for u(e) = 0) of the state variables x(t) and the output y(t). [4 marks] (d) For another system with the following characteristic question A(s) s²+ks²+ks +8-0 Determine the range of k to make the system stable using Routh-Hurwitz criterion. [4 marks]