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1 ISSN Vol.04,Issue.06, June-2016, Pages: Design and Development of IMC Tuned PID Controller for Disturbance Rejection of Pure Integrating Process G.MADHU KUMAR 1, V. SUMA DEEPTHI 2 1 PG Scholar, Malla Reddy Engineering College, India, gurrammadhukumar@gmail.com. 2 Assistent Professor, Malla Reddy Engineering College, India, sumadeepthi.veeraganti@gmail.com. Abstract: In this paper we introduce a PID controller for chemical reactors and liquid level systems for pure integral process reducing the disturbance in the system with step change in the input variable. The proposed controller increases the robustness of the control structure with very good disturbance mitigation. The derivation and design of the IMC (Internal Model Control) is represented in MATLAB Simulink software with all results and graphical representations. Keywords: Integrating Process, IMC Performance, PID, Filter, Robustness Disturbance Rejection, Sensitivity Set Point. I. INTRODUCTION In process control applications, model based control systems are often used to track set points and reject low disturbances. The internal model control (IMC) philosophy relies on the internal model principle which states that if any control system contains within it, implicitly or explicitly, some representation of the process to be controlled then a perfect control is easily achieved. In particular, if the control scheme has been developed based on the exact model of the process then perfect control is theoretically possible. Fig.1. Classical Feedback Structure with Plant and Controller. Output = Gc. Gp. Set-point (multiplication of all three parameters) Gc = controller of process Gp = actual process or plant Gp* = model of the actual process or plant A controller Gc is used to control the process Gp. Suppose Gp* is the model of Gp then by setting: Gc =inverse of Gp* (inverse of model of the actual process) And if Gp = Gp* (the model is the exact representation of the actual process) Now it is clear that for these two conditions the output will always be equal to the set point. It show that if we have complete knowledge about the process (as encapsulated in the process model) being controlled, we can achieve perfect control. This ideal control performance is achieved without feedback which signifies that feedback control is necessary only when knowledge about the process is inaccurate or incomplete. Although the IMC design procedure is identical to the open loop control design procedure, the implementation of IMC results in a feedback system. Thus, IMC is able to compensate for disturbances and model uncertainty while open loop control is not. Also IMC must be detuned to assure stability if there is model uncertainty. The distinguishing characteristic of IMC structure is the incorporation of the process model which is in parallel with the actual process or the plant. Also we consider that * is generally used to represent signals associated with the model. As stated above that that actual process differs from the model of the process i.e. process model mismatch is common due to unknown disturbances entering into the system. Due to which open loop control system is difficult to implement so we require a control strategy through which we can achieve a perfect control. Thus the control strategy which we shall apply to achieve perfect control is known as INTERNAL MODEL CONTROL (IMC) strategy. II. DESIGN OF PID CONTROLLER The IMC design procedure is exactly the same as the open loop control design procedure. Unlike open loop control, the IMC structure compensates for disturbances n model uncertainties. The IMC tuning (filter) factor lem is used to detune for model uncertainty. 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, particularly for the disturbances that occur at the process inputs. A modification of the design procedure is developed to improve input disturbance rejection IJIT. All rights reserved.

2 G.MADHU KUMAR, V. SUMA DEEPTHI A. IMC Based PID Structure In the IMC structure the point of comparison between the process and the model output can be moved as shown in the figure below to form a standard feedback structure which is nothing but another equivalent feedback form of IMC structure know n as IMC based PID structure. Fig.2. IMC Controller Structure Tolerance of model uncertainty is called robustness. Like open loop control the disadvantage compared with standard feedback control is that IMC doesn t handle integrating or open loop unstable systems. The IMC structure can be rearranged to form a standard feedback control system that can easily handle open loop unstable system as not the case with IMC. This modification of the IMC design procedure is developed to improve the input disturbance rejection. The IMC based PID structure which uses a standard feedback structure uses the process model in an implicit manner i.e. PID tuning parameters are often adjusted based on the transfer function model but it is not always clear how the process model affects the tuning decision. In the IMC procedure the controller Qc(s) is directly based on the good part of the process transfer function. Also the IMC formulation generally results in only one tuning parameter, the close loop time constant (filter tuning factor). The IMC based PID tuning parameters are then the function of this time constant. The selection of the closed loop time constant is directly related to the robustness (sensitivity to the modular of the closed loop system). Also, for open loop unstable processes it is necessary ti implement the IMC strategy in standard feedback form, because the IMC suffers from internal stability problems. Though the IMC based PID controller will not give the same performance when there are process time delays because the IMC based PID procedures uses an approximation for the dead time. But if the process has no time delays and the inputs do not hit a constraint then the IMC based PID controller give the same performance as does the IMC. III. DERIVATION AND PERFORMANCE ASSESMENT We know that in IMC controller design plant model is factorized into invertible/non-invertible parts.the proposed controller with given characteristic equations is derived as the design of the IMC controller is (2) The structure of the ideal feedback controller is Since the resulting controller does not have a standard PID controller form, the main issue is to design the PID controller that approximates the equivalent feedback controller most closely. Since has an integral term, it can be expressed as (4) Using McLaren series expansion an S gives The first term in the eqn. (5) can be interpreted as the standard PID controller, which is given as The DIP can be modeled by considering the integrator as a stable pole near zero. This is necessary it is not possible to apply the aforementioned IMC procedure for DIP. Since the term α disappears at s=0. Therefore the DIP can be approximated to FOPDT as (1) (3) (5) (6) (7) whereᵩ is an arbitrary constant with a sufficient large value Considering the filter used by Gopi et al for the design of the IMC tuned PID controller. (8) Fig.3. IMC Based PID Control Structure (9)

3 Design and Development of IMC Tuned PID Controller for Disturbance Rejection of Pure Integrating Process Therefore IMC controller IV. SIMULATION RESULTS AND GRAPHS (10) (11) (12) Fig.4. Simulink Design of Proposed IMC PID Controller. Case 1: (13) (14) The analytical PID formula is obtained from eqn.(15) as Table I (21) (15) (16) (17) The value of the extra degree of freedom α is selected so that it cancels out the open loop pole at s=-1 τ, that causes sluggish response to the load disturbance. Therefore α is chosen so that term has a zero at the pole of Fig.5. Load disturbance Response for Case 1. (18) Here τ=ψ (19) On simplification it yields, (20) Fig.6. Controller Response for Disturbance in Case 1.

4 Case 2: Table II. G.MADHU KUMAR, V. SUMA DEEPTHI uniform comparison, the controllers are designed to possess identical robustness on the grounds of maximum sensitivity MS. VI. CONCLUSION (22) An IMC filter of the form is proposed for the design of PID controller based on IMC principle to enhance disturbance rejection efficiency. The pure integrating process with delay time is modeled as first-order process with time delay for the design of the controller. The tuning formula for the proposed PID tuning is summarized as (24) (25) (26) Fig.7. Load Disturbance Response for Case 2. Fig.8. Controller Response for Disturbance in Case 2. V. MAXIMUM SENTIVITY MODEL MISMATCH (23) The maximum sensitivity model mismatch is the inverse of the shortest distance from Nyquist plot to the critical point The stability margin of the system is enhanced with the decrease in MS value. For uniform comparison, the controllers are designed to have same MS value by adjusting the λ, which affects KP alone. The range of MS for a satisfactory performance of the control system is The performances of the PID controller based on IMC method with conventional filter projected by and filter proposed by and tuning techniques proposed for IPDT by and are compared with proposed method for conciseness, and for (27) A set point filter is suggested to reduce the overshoot in the set point response as the proposed method is basically designed for disturbance rejection. λ the closed-loop time constant is the single adjustable tuning parameter for a given process/plant model, and it provides the compromise between performance and robustness. VII. REFERENCES [1]Anusha, A. V. N. L., & Rao, A. S. (2012). Design and analysis of IMC based PID controller for unstable systems for enhanced closed loop performance. Proceedings of the IFAC Conference Advances in PID control (PID 12). [2]Arbogast, J. E., & Cooper, D. J. (2007). Extension of IMC tuning correlations for non-self regulating (integrating) processes. ISA Transactions, 46(3), [3]Chia, T. L., & Lefkowitz, I. (2010). Internal model-based control for integrating processes. ISA Transactions, 49(4), [4]Chien, I. L., & Fruehauf, P. S. (1990). Consider IMC tuning to improve performance. Chemical Engineering Progress, 86, [5]Desborough, L. D., & Miller, R.M. (2002). Increasing customer value of industrial control performance monitoring Honeywell s experience. Chemical Process Control - VI, AIChE Symposium Series No , Tucson, Arizona, USA. (pp ). [6]Eris, O., & Kurtulan, S. (2011). A new PI tuning rule for first order plus dead-time systems. IEEE Africon, 11, 1 4. [7]Garcia, C. E., & Morari, M. (1982). Internal model controls 1. A unifying review and some new results. Industrial Engineering Chemical process Design and Development, 21, 308.

5 Design and Development of IMC Tuned PID Controller for Disturbance Rejection of Pure Integrating Process [8]Gopi Krishna Rao, P. V., Subramanyam, M. V., & Satyaprasad, K. (2013). Model based tuning of PID controller. Journal of Control & Instrumentation, 4(1), [9]Gopi Krishna Rao, P. V., Subramanyam, M. V., & Satyaprasad, K. (2014a). Design of IMC-PID controller with improved filter for disturbance rejection. Systems Science & Control Engineering: An Open Access Journal, 2(1), doi: / [10]Gopi Krishna Rao, P. V., Subramanyam, M. V., & Satyaprasad, K. (2014b). Design of cascaded IMC-PID controller with improved filter for disturbance rejection. International Journal of Applied Science and Engineering, 12(2), [11]Gopi Krishna Rao, P. V., Subramanyam, M. V., & Satyaprasad, K. (2015). Time delay approximation: Its influence on the structure and performance of IMC-PI/PID controller. Intelligent Computing, Communication and Devices, Advances in Intelligent Systems and Computing, Springer India, 308, [12]Horn, I. G., Arulandu, J. R., Christopher, J. G., VanAntwerp, J. G., & Braatz, R. D. (1996). Improved filter design in internal model control. Industrial & Engineering Chemistry Research, 35, [13]Jin, Q. B., & Liu, Q. (2014). Analytical IMC-PID design in terms of performance/robustness trade-off for integrating processes: From 2-Dof to 1-Dof. Journal of Process Control, 24(3),

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