31.미분방정식 로 표시되는 계의 시스템행렬과 입력행렬은?
정답
해설
Let's say that we have a general 2rd order differential equation in terms of input u(t) and output y(t): y''(t) + a1 x y'(t) + a0 x y(t) = b0·u(t) We can create the state variable vector x in the following manner: x1 = y(t)} x2 = y'(t) Which now leaves us with the following 2 first-order equations: x1' = x2 x2' = y''(t) Now, we can define the state vector x in terms of the individual x components, and we can create the future state vector as well: x = [x1], x' = [x1'] [x2] [x2'] And with that, we can assemble the state-space equations for the system: x' = [0 1]·x(t) + [0]·b0·u(t) [-a1 -a0] [1] y(t) = [1 0 0]·x(t) Granted, this is only a simple example, but the method should become apparent to most readers. 그래서, 다음 식에 변수 a0, a1, b0를 대입하면 답이 보기 1번임을 알 수 있음! -다음- x' = [0 1]·x(t) + [0]·b0·u(t) [-a1 -a0] [1] 다시 풀어 써보면, [x1'] = [0 1]·[x1] + [0]·u(t) [x2'] [-1 -2] [x2] [3] 위 행렬식을 계산해보면, 문제에 주어진 미분 방정식을 만족함을 알 수 있음!