Solution Found!
A process including sensor and control valve can be (I)
Chapter 12, Problem 12.7(choose chapter or problem)
A process including sensor and control valve can be modeled by a fourth-order transfer function:
\(G(s)=\frac{1}{(s+1)(0.2 s+1)(0.04+1)(0.008 s+1)}\)
(a) Design PID controllers using two design methods:
(i) A second-order-plus-time-delay model using the model reduction approach proposed by Skogestad (Section 6.3) and the modified IMC tuning relation in Table 12.5.
(ii) The Tyreus-Luyben settings in Table 12.6.
(b) Evaluate the two controllers by simulating the closed loop responses to a unit step change in a disturbance, assuming that \(G_{d}(s)=G(s)\)
Questions & Answers
QUESTION:
A process including sensor and control valve can be modeled by a fourth-order transfer function:
\(G(s)=\frac{1}{(s+1)(0.2 s+1)(0.04+1)(0.008 s+1)}\)
(a) Design PID controllers using two design methods:
(i) A second-order-plus-time-delay model using the model reduction approach proposed by Skogestad (Section 6.3) and the modified IMC tuning relation in Table 12.5.
(ii) The Tyreus-Luyben settings in Table 12.6.
(b) Evaluate the two controllers by simulating the closed loop responses to a unit step change in a disturbance, assuming that \(G_{d}(s)=G(s)\)
ANSWER:
Step 1 of 13
We are given the following information:
The transfer function of a process including a control valve and a sensor is given by:
\(G=\frac{1}{(s+1)(0.2 s+1)(0.04 s+1)(0.008 s+1)}\)
We will solve the problem in the following steps:
- First the transfer function will be reduced to a second order transfer function using Skogestad's half rule.
- Refer to table 12.1 for the IMC approach to obtain the PID controller settings.
- get the values of the ultimate period and ultimate gain.
- Refer to table 12.4 for the Tyreus-Luyben to obtain the PID controller settings.
- Simulate the step response from the block diagram of the closed loop system.