计算机控制技术-(2.5、2.6、3.1、3.2).pptVIP

Closed loop trans. Function: Output of the system: i.e. y(0)= y(1)= y(2)= y(3)= After two sampling intervals, y(k)=r(k) at the sampling instants. [Notice the ripple between sampling instants ] If the input signal is changed to unit parabolic, then the output will be: That is to say: A deadbeat controller is designed with respect to a specific input signal. When other input signals are applied, the deadbeat control system is no longer to keep its “deadbeat” characteristic. 3.2.3 Deadbeat controller design for the systems with unstable zeros/poles and time delay Previous design methods for deadbeat controller are derived on the basis of assumptions. Without the assumptions (limitations), Gk(Z) can be generally expressed as: Where, zi = zeros of Gk(z) pi = poles of Gk(z) z-d = time delay --- 3.2.6 Substitute Eqt. 3.2.6 into Eqt. 3.2.3, we have: Discussions: D(z) contains zd, indicating that the output of controller is d steps ahead of its input 2) Unstable zeros of Gk(z) become unstable poles of D(z) --physically unable to implement -- leading to unstable D(z) 3) Unstable poles of Gk(z) become unstable poles of the closed loop system -- leading to unstable GB(z) Therefore, new design rules should be applied to the system, which are concluded as: 1) To ensure that closed loop system is stable, use GE(z)’s zeros to cancel the unstable poles of the Gk(z) 2) GB(z) should contain Gk(z)’s unstable zeros to ensure the stability of D(z) 3) GB(z) should contain the term Z-d of Gk(z) to eliminate the factor Zd in D(z) To summarize, we should choose GE(z) and GB(z) that satisfy: Where: pi and zi are unstable poles and zeros of Gk(z), while F1(z) and F2(z) are z polynomials to be decided. -- normally the simplest , or equivalent, with the lowest degree Note: Because the GB(z) contains factor z-d in this case, system response time will be longer than the previous case. In other words, the system is not precisely a de