Dear Janani

your response generally is an actual (output) signal or  the difference between actual and reference signals it means error. so if you want to know about trajectory follow you can check desired and actual signal, if you want to know about error you can check error response,........

Regards

The output of the PID controller is the control signal.

If you want to monitor the response, say in simulink then insert the scope at the output of the PID controller. And, if you want to have a transfer function from the control input to the plant output you can work it out using may be block diagram reduction or signal flow graph 

One of the inputs to the plant can act as control signal. Its response depends on the gains of the PID controller. as output of PID control is the control signal maipulating the plant response.

regards

The Ziegler method is used for deciding the PID gains of the limited 2nd order system. I dont understand that you got the output response of the plant by using the Ziegler method. Probably, you expected the specification of the response (natural freq. and damping --> rising, settling, peak times, etc) from the Ziegler method.

i think the control signal you mentioned is the real output of an actuator. If my understanding is right, the PID controller output is just a command to the actuator. The actuator movement is different from the controller output (command) due to the actuator dynamics itself and the interaction between the actuator and surrounding environment. For example, the controller surface of an airplane moves differently from the PID controller command due to actuator delay and aerodynamic forces exerted from the interaction with atmosphere.

By control signal you mean the signal which is going to the plant. It is the signal which is output of PID block (or PID controller.) The output of the plant is actually the response . You can modify responses by modifying the input to the plant by modifying values of PID controller. simple. all the best