This is to certify that the project report entitled “INTERNAL MODEL CONTROL (IMC) AND IMC-BASED PID CONTROLLER” submitted by A nki t Por wal (Rol No a n d V ip i n V ya s (R o l l No) in the partial compliance of the requirements) for the award of Bachelor of Technology in Electronics and Instrumentation Engineering during session 2006-2010 at National Institute of Technology, Rourkela (Respected University) and is an authentic work executed by them under my supervision and guidance Sim1: SISO simulation for IMC 1st order (tau=1.5) 27 Sim2: SISO simulation for IMC 1st order (tau=2.5) 27 Sim3: SISO simulation for IMC 1st order (tau=3.5) 28 Sim4: SISO simulation for IMC 2nd order (tau=1) 29 Sim5: SISO simulation for IMC 2nd order (tau=2) 29 Sim6: SISO simulation for IMC 2nd order (tau=3) 30 Sim7: Output variable response for IMC 1st order system 36 Sim8: Manipulated variable response for IMC 1st order system 36 Sim9: Output variable response for IMC 2nd order system 38 Sim10: Manipulated variable response for IMC 2nd order system 38 Sim11: Output variable response for IMC based PID 1st order system 46 Sim12: Output variable response for IMC based PID 2nd order system 48. Also the IMC-PID controller allows good setpoint tracking, but sulky disturbance response especially for the process with a small time-delay/time-constant ratio.
But for many process control applications, disturbance rejection for unstable processes is much more important than set point tracking. In this thesis, we propose an optimal IMC filter to design an IMC-PID controller for better tracking of the set points of unstable processes. However, IMC results in a long settling time of load disturbances for dominant processes with a delay, which are not desirable in the regulation industry.
Then we tried tuning our IMC controller for different values of the filter tuning factor. Thus, in our approach to IMC and IMC-based PID controller to be used in industrial process control applications, the optimum filter structure exists for each specific process model to provide the best PID performance.
INTRODUCTION TO INTERNAL MODEL CONTROL (IMC)
- IMC basic structure
- IMC parameters
- Chapter 2
- Using SISO TOOL for IMC implementation IMC Design with Automatic Tuning
- No Values of time constant (tau) Settling time (in sec)
- Chapter 3
The internal model control (IMC) philosophy relies on the internal model principle which states that if any control system contains, implicitly or explicitly, some representation of the process to be controlled, perfect control is easily achieved. In particular, if the control scheme is developed based on the exact model of the process, perfect control is theoretically possible. This shows that if we have complete knowledge about the process (as contained in the process model) being controlled, we can achieve perfect control.
This ideal control performance is achieved without feedback, meaning that feedback control is only necessary when knowledge of the process is inaccurate or incomplete. The characteristic feature of the IMC structure is the incorporation of the process model, which is parallel to the actual process or plant. We will say that a model is perfect if the process model is the same as the actual process, i.e.
So if the controller Qc is stable and the process Gp is stable, the closed loop system will be stable. But in practical cases there are always disturbances and uncertainties and therefore the actual process or installation always differs from the model of the process. If the actual process is the same as the process model, i.e. Gp(s) = Gp*(s), then the feedback signal d*(s) is equal to the unknown disturbance.
So for this case d*(s) can be considered as missing information in the model implies and therefore can be used to improve the control for the process. Also to improve the stability of the system the effect of model mismatch should be minimized. Since the mismatch between the actual process and the model usually occurs at the high frequency end of the systems frequency response, a low-pass Gf(s) filter is usually added to mitigate the effects of the process model mismatch.
Thus, the internal model controller is usually designed as an inverse process model in series with a low-pass filter, i.e. where the filter order is usually chosen to keep the controller adequate and to avoid excessive differential control. SISO TOOL is a graphical user interface (GUI) that allows us to design single-input/single-output (SISO) compensators by graphically interacting with root-place, Bode plots of an open-loop system.
Imported systems can include any of the feedback structure diagram elements located to the right of the Current Compensator panel. Note: G1 is the actual plant used; G2 is an approximation of the real plant and is used as a plant model in the IMC structure.
IMC DESIGN PROCEDURE
- IMC design procedure
- FACTORIZATION
- IDEAL IMC CONTROLLER
- ADDING FILTER
- LOW PASS FILTER f(s)
- IMC design for 1 st order system
- Simulation plot for IMC 1 st order system a) Output variable response
- IMC design for 2 st order system
- Simulation plot for IMC 2 st order system a) Output variable response
- Chapter 4
The KPM design procedure is exactly the same as the open-loop control design procedure. It should be noted that the standard IMC design procedure is focused on set point responses, but good set point responses do not guarantee good disturbance rejection, especially for disturbances occurring at process inputs. Like open-loop control, the disadvantage compared to standard feedback control is that IMC does not handle integrative or open-loop unstable systems.
A factor containing a right-hand plane (RHP) or zeros or time delays become the poles in the inverts of the process model when designing. The ideal IMC controller is the flip side of the invertible part of the process model. A transfer function is correct if the order of the denominator is at least as large as the order of the numerator.
If they are exactly of the same order, the transfer function is said to be semi-proper. If the order of the denominator is greater than the order of the numerator, the transfer functions are strictly correct. To improve the robustness of the system, the effect of model mismatch should be minimized.
Since mismatch between the actual process and the model usually occurs at the high-frequency end of the system frequency response, a low-pass filter f(s) is usually added to mitigate the effects of process model mismatch. Where blade is the filter tuning parameter to change the speed of the response of closed loop system. If we focus on good detection of ramp setpoint changes, the filter of the form used is.
Focusing on good step input load disturbance rejection is the use of a shape filter. Let us now apply the above IMC design procedure to a first-order system with a given process model. 3.3.1 Simulation display for the IMC system of the 1st order a).
IMC BASED PID
- IMC based PID structure
- IMC based PID design procedure
- FACTORIZATION
- IDEAL IMC CONTROLLER
- ADDING FILTER
- LOW PASS FILTER [f(s)]
- Equivalent standard feedback controller
- Comparison with standard PID controller Now we compare with PID Controller transfer function
- IMC based PID for 1 st order system
- Simulation for IMC based PID 1 st order system
- IMC based PID for 2 nd order system
- Simulation for IMC based PID 2 nd order system
The structure of the KPM can be rearranged to form a standard feedback control system that can easily handle an unstable open-loop system, as is not the case with the IMC. This modification of the KPM design procedure was developed to improve input disturbance rejection. The IMC-based PID structure which uses a standard feedback structure uses the process model in an implicit way, i.e.
PID tuning parameters are often adjusted based on a transfer function model, but it is not always clear how the process model affects the tuning decision. In the IMC process, the Qc controller is directly based on the good part of the process transfer function. Also, the IMC formulation generally results in only one tuning parameter, the closed-loop time constant (filter tuning factor).
The choice of the closed-loop time constant is directly related to the robustness (sensitivity to the modularity of the closed-loop system). Also, for open-loop unstable processes, it is necessary to implement the IMC strategy in standard feedback form, because the IMC suffers from internal stability problems. Although the IMC-based PID controller will not provide the same performance when there are process time delays because the IMC-based PID procedures use an approximation for the dead time.
But if the process has no time delays and the input does not hit a limit, the IMC based PID controller gives the same. In the IMC structure, the comparison point between the process and the model output can be shifted as shown in the figure below to form a standard feedback structure which is nothing but another equivalent feedback form of IMC structure known as IMC-based PID- structure not. This means factoring a transfer function into reversible (good stuff) and non-reversible (bad stuff) parts.
Similarly, for the 2nd order, we compare it with the standard transfer function of the PID controller that it gives. Let us now apply the above IMC-based PID design procedure to a first-order system with a given process model. Now let's apply the above IMC-based PID design procedure to a second-order system with a given process model. is the transfer function for the equivalent standard feedback controller.
APPLICATIONS
CONCLUSION &
FUTURE WORKS
