Implementing 2DOF pole-placement controller using PRBS model, virtually

For deriving the Two degrees of freedom control law, please refer to the chapter 6.2 The controller was designed for the given transient conditions, rise time = 10 sec, overshoot = 0.1. The experimental result and performance of the controller for setpoint temperature change from 38.00 to 43.00 degree C, i.e. 5 degree C positive step change, has been shown below in Fig 7.10. The controller designed is not derived for the model explained in earlier sections.

Figure 7.10: 2dof controller response

The parameters for the 2-DOF pole-placement controller obtained are shown here

$$Tc = 1 - 1.9444137 z^{ -1} + 0.9447818 z^{ -2}$$

$$Sc = 0.0337719 - 0.0656666z^{ -1}+ 0.0319071z^ { -2}$$

$$Rc = 10^{-9} (4377900 - 12034140 z^{ -1} + 11094713 z^ {-2} - 3436740.5 z^{-3} + 3.469D^{-09} z ^{-4}$$

$$- 147850.06 z^ {-5} + 146117.57 z^{ -6} )$$

$$\gamma = 0.0337719$$

As can be observed from the graph of temperature vs. time (third subplot) in Fig 7.10, the overshoot criteria was satisfied very easily. The rise time criteria is observed to be more than 30 sec. This can be satisfied with experimentation. The paramenters are computed by the file twodof_para.sce.

The steps to be followed to conduct PRBS test experiment virtually remains same as explained in section 1.1. only for the following differences

• Step1: The working directory is prbs/controller. Open this directory.
• Step2: Same
• Step3: Same
• Step4: Switch to the controller experiment directory and double-click on the file prbs.sce. This will launch scilab and also open the file prbs.sce in the scilab editor. Linux users will have to launch scilab manually. They also have to change the working directory to controller and then open the prbs.sce file in the scilab editor.
• Step5: Load the functions available in common files directory by executing the command getd<space>..\..\common_files
• Step6: Execute the file prbs.sce. Expect the prbs test xcos diagram to open automatically. If this doesnt happen, check the scilab console for error message. The values of Rc, Sc, Tc and $\gamma$ are to be entered in the xcos diagram.
• Step7: Execute the prbstest xcos diagram.
• Step8: Same