Shown below is the feedback system for this problem.

        The transfer function for the system being controlled - the plant - is given by:

You need to investigate the behavior of this system.  Before you proceed you need to consider the following questions.

• The plant has two real poles, and two real poles do not give oscillatory response.  Is it possible for this system to have an oscillatory response?

Check both answers in the Yes-No set of buttons.  You should realize that the closed loop transfer function (i.e. the transfer function for the whole system with the loop closed) will have the same order as the plant (since the controller is a pure gain) but that it might well happen that the closed loop poles are complex.  We have built a simulator for you to check some of these ideas.

        In this simulator you can adjust the gain, K, in the controller.  Initially, K is set to 1.0.

• Run the simulator with K = 1.0.
• Input K = 5 and run the simulator.
• Redo for K = 10, 20 and 50.
• Explain the results.