First, we have toĬlose the loop of the transfer function by using the feedback command. We would now like to analyze the closed-loop response of the system without any additional compensation. Note the absence of the pole and zero near z = 0. Applying the minreal command, therefore, produces the following reduced order transfer function. Will help to avoid numerical difficulties in MATLAB. Cancellation of this pole and zero will reduce the order of our transfer function and This cancellation in the transfer function can be accomplished by applying the minreal command with a tolerance of 0.001. Adding the following commands to your m-file and running in the MATLAB command window generatesįrom the above, notice that there is a pole and zero very near to z = 0 that effectively cancel. Refer to the Introduction: Digital Controller Design page for further details. In this example, we will assume a zero-order hold ( zoh) circuit. The c2d command requires three arguments: a system model, the sampling time ( Ts), and the type of hold circuit. MATLABĬan be used to achieve this conversion through the use of the c2d command. In this case, we will convert the given transfer function from the continuous Laplace domain to the discrete z-domain. Of the required time constant and 1/40 of the required settling time. A sample time of 0.001 seconds is specifically 1/100 To the speed that will be achieved by the resultant closed-loop system. This sampling period is also fast compared Seconds (frequency of 1000 Hz) is significantly faster than the dynamics of the plant. Therefore, choosing a sampling period of 0.001 The gain crossover frequency of the plant is approximately 5 Hz. The poles of the plant (or its frequency response), it is clear that the pole at -1.45e06 contributes very little to the response The use of the zpk command above transforms the transfer function into a form where the zeros, poles, and gain can be seen explicitly. Within the MATLAB command window will generate the output shown below. Create a new m-file and add the following MATLAB code (refer to the main problem for the details of getting these commands). Let's create a continuous-time model of the plant. That the sampling frequency be fast compared to the dynamics of the system in order that the sampled output of the systemĬaptures the system's full behavior, that is, so that significant inter-sample behavior isn't missed. In choosing a sampling period, it is desired Necessary to choose a frequency with which the continuous-time plant is sampled. The first step in the design of a digital control system is to generate a sampled-data model of the plant. No steady-state error, even in the presence of a step disturbance inputĬreating a sampled-date model of the plant.
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