PDF《实验三 PID 控制技术的》

10 N.s/m ? k =

20 N/m ? F(s) =

1 Plug these values into the above transfer function The goal of this problem is to show you how each of Kp, Ki and Kd contributes to obtain ? Fast rise time ? Minimum overshoot ? No steady-state error Open Open Open Open- - - -loop step response loop step response loop step response loop step response Let'

s first view the open-loop step response. Create a new m-file and add in the following code: num=1;

den=[1

10 20];

step(num,den) Running this m-file in the Matlab command window should give you the plot shown below. The DC gain of the plant transfer function is 1/20, so 0.05 is the final value of the output to an unit step input. This corresponds to the steady-state error of 0.95, quite large indeed. Furthermore, the rise time is about one second, and the settling time is about 1.5 seconds. Let'

s design a controller that will reduce the rise time, reduce the settling time, and eliminates the steady-state error. Proportional control Proportional control Proportional control Proportional control From the table shown above, we see that the proportional controller (Kp) reduces the rise time, increases the overshoot, and reduces the steady-state error. The closed-loop transfer function of the above system with a proportional controller is: Let the proportional gain (Kp) equals

300 and change the m-file to the following: Kp=300;

num=[Kp];

den=[1

10 20+Kp];

t=0:0.01:2;

step(num,den,t) Running this m-file in the Matlab command window should gives you the following plot. Note: The Matlab function called cloop can be used to obtain a closed-loop transfer function directly from the open-loop transfer function (instead of obtaining closed-loop transfer function by hand). The following m-file uses the cloop command that should give you the identical plot as the one shown above. num=1;

den=[1

10 20];

Kp=300;

[numCL,denCL]=cloop(Kp*num,den);

t=0:0.01:2;

step(numCL, denCL,t) The above plot shows that the proportional controller reduced both the rise time and the steady-state error, increased the overshoot, and decreased the settling time by small amount. Proportional Proportional Proportional Proportional- - - -Derivative control Derivative control Derivative control Derivative control Now, let'

s take a look at a PD control. From the table shown above, we see that the derivative controller (K........