T
A2=


(8-10)


were the coefficients of the difference equation.

 A simulation of both the continuous and discrete versions of the lag-lead compensator

was conducted for verification of the discretization and for selection of a sampling time that

would best duplicate the performance of the continuous compensator. Initially, the continuous

controller response to a step input was determined via inverse Laplace transformation. In the

continuous time domain, the lag-lead controllers were functions of the system gain, K, the lag

and lead time constants, Ti and Td, and time, t, as in


 H(t) = K + i -i- eV;)
 Ti Td T dd (8-11)

The discrete difference equation (equation 8-7) was programmed for a simulated response to a

unit step input. A comparison was conducted for various values of Kc, Ti, and Td. Since vision

data was updated at 60 HZ, a discrete sampling time of 0.01667 sec (1/60 sec) was initially

chosen. Typical responses of the controllers along with the differences between the signals are

presented in Figure 8.3. For this presentation, the controller parameter values for the joint 0

position and vision controllers were used. Thus, these simulations were repeated for the final,

tuned controller parameters after the tuning process was complete. These plots indicated that

the discrete version of the lag-lead controller had a maximum error of 22 percent which

decreased to less than 0.6 percent in less than 0.08 sec or 5 sampling periods. These response

curves were used to verify that the discrete version of the lag-lead controller did adequately

imitate the performance of the continuous-time controller and that the theory of the continuous

domain controller could be used in tuning the discrete controller.

 After the discretized version of the lag-lead compensator was verified, a section was

added to the software environment to aid in tuning the discrete lag-lead compensator. This

section calculated the coefficients of the difference equations from the analog parameters Ti, Td,