METHODOLOGY FOR REDUCING THE CONTROL LOOPS OSCILLATION AT AN IRON ORE PROCESSING PLANT Lúcio Fábio Passos 1 lucio.passos@atan.com.br Bernardo Soares Torres 1 bernardo.torres@atan.com.br Vicentino José Pinheiro Rodrigues 2 vicentino.rodrigues@cvrd.com.br 1 ATAN Sistemas de Automação 2 Companhia Vale do Rio Doce Abstract In continuous process industries, oscillation cycles generally spread for the process affecting the quality and the efficiency of the plant. These cycles can be caused by inadequate tuning of the controllers, problems in actuators or coupling between loops. This work presents a method to track and to detect the causes of the main oscillation cycles among 80 loops from an iron ore processing plant through the use of dedicated software for continuous monitoring and automatic diagnosis of control loops. Keywords: process optimization, control loops, variability, oscillation 5º International Meeting of Instrumentation, Systems and Automation ISA Show 2005, São Paulo.
1 INTRODUCTION The variability of a control loop is one of the most important and common indexes used to measure the performance of a process. It is defined as the dispersion of a process variable in a period of time. The smaller its value, the better the loop performance and, consequently, the better the quality of the final product and the smaller the operational costs. In general, when observing a process variable, one can see that the variable shows random patterns. However, this appearance can be the result of an overlapping of many distinct and defined cycles. This way, the identification of oscillation periods through the use of temporal graphic inspection, generally, is not trivial. Figure 1 exemplifies an oscillatory signal and the cycles that compose it. In case of elimination of an oscillation cycle, the loop variability will be reduced proportionally to the contribution of this cycle in the total spectral power of the signal. Decreasing the variability means that the set-points can be set to its optimum values, near the safety limits of the process without the risk of exceeding them. Figure 1: Signal with overlapped oscillation cycles In continuous process industries, such oscillation cycles generally spread through the process affecting the quality and the efficiency of the plant. Once detected, the oscillation cycles can be eliminated if their main cause is found. This diagnosis becomes very complex when the number of control loops involved is huge. Computational tools can make this work a lot easier. By means of sophisticated mathematic algorithms, it is possible to analyze the control signals and to determine the most probable oscillation source. This work presents a method to track and eliminate oscillation cycles through the use of dedicated software for continuous monitoring and automatic diagnosis of control loops.
2 MÉTHODS In this section, three techniques used on control loops analysis will be described. 2.1 Spectral density Using spectral analyses tools, it is possible to determine the main oscillation cycles of a loop. It describes the way that the signal power of a temporal series is distributed in frequency domain. If the set-point is constant, in a perfect control, the spectrum would be uniformly distributed over all frequencies, without peaks. This indicates that the signal contains only white noise. However, frequently, the controllers are not adequately projected, or they are not able to reject some disturbances (frequencies higher than the cut frequency of the controller). These un-rejected disturbances usually appear detached in the spectral analysis. Figure 2 shows a temporal graphic and the frequency spectrum of an oscillatory signal in the control loop of the foam level in a flotation column. The two cycles that most contribute for the variability of this signal, detached on the graphic of spectral analyses, have periods of 347 and 430 seconds. Figure 2: Spectral Density 2.2 Detecting and diagnosing oscillation The oscillation diagnosis consists in appointing the probable cause of cycles that have the biggest spectral power of the signal. In general, these cycles of oscillation are caused by inherent events to the process like load variations, batch, vibrations, inadequate tuning or actuators problems (generally stiction or hysteresis). When these cycles affect other control loop, which is very common, it is said that there are cycles caused by coupling.
Once there is a recognized pattern, this analysis can directly appoint to the cause of the problem (Gerry, 1998 [1]). For example, if the oscillation is predominantly sinusoidal, your source is probably an aggressive tuning or a disturbance that can t be rejected by the controller. Differently, loops with actuator problems (hysteresis, stiction, etc) present a spectrum with infinite harmonics, typical of nonlinear signals. Figure 3a shows an example of oscillation caused by actuator problems. It refers to a water pressure loop (PIC13402). In Figure 3b, it was identified oscillation caused by tuning on the rougher air flow loop (FIC6876). a b Figure 3: Typical frequency spectrum of an actuator with excessive non-linearity (A) and inadequate tune (B).
The summary of the diagnosis mechanisms are listed below: Tuning-Oscillation: Oscillation generated by an aggressive tuning. Shinskey [1] presents a useful relation to determine the oscillation caused by an inadequate controller adjustment. According to him, the natural period of oscillation (τn) of a control loop is of 2 to 4 times its dead time (τd), depending on the relation between the dead time and the dominant time constant of the process (τ1). This relation is summarized in the equation below. 2 τ d τ n τ d τ d τ 4 + 1 Therefore, oscillation caused by tuning generally presents sinusoidal cycles with periods of 2 to 4 times the dead time of the process. Valve-Oscillation: It indicates that the origin of the oscillation can be the final control element. The process variables and the controller output present non-sinusoidal oscillation resulted by a nonlinear behavior. This can be identified by the presence of infinity harmonics on the frequency spectrum. In this case, detailed tests (stiction, hysteresis, etc) should be performed to confirm the diagnosis. Load-Oscillation: The origin of the oscillation is found in the load or in the load upsets. In general, this is the cause of oscillation when both of the other two cases can t be applied. 2.3 Relative Response Time It is known that the controllers act like high-pass filters, attenuating frequencies lower than its cut frequency (approximately the inverse of the closed loop time constant). This time constant can be estimated on-line considering the speed that the loop rejects a disturbance. The assessment Relative Response Time (RRT), proposed by Expertune Inc [2], is a relative indicator of the speed of a control loop. It is calculated using the frequency response to a disturbance. The smaller its value, the faster is the loop. Figure 4, on right, shows the response of a loop to a load upset. At this moment the loop presents an oscillation with period of 15 seconds. This value converted in cycles/seconds (1/15=0.068) corresponds to a frequency of maximum amplitude in the bode diagram of the load upset response. Figure 4: Speed of the control loop measured by the Relative Response Time In some cases, two loops can oscillate by the fact that they are interacting. The actuation of one generates oscillation in the other and vice-versa. The RRT index can be used to identify these cases. The RRT of a loop can be adjusted by the PID tuning. In order to avoid the interaction, is recommended to keep the relation between the RRT larger than a factor of 3.
3 METHODOLOGY APPLIED IN AN ORE PROCESSING PLANT The techniques presented were applied in a mining treatment plant of Companhia Vale do Rio Doce in Itabira, state of Minas Gerais (Brazil) with the objective of analyze and optimize about 80 control loops. During a period of 5 months, a software was used to read the process data and to generate assessments and diagnoses of the control loops. Spectral analysis, oscillation diagnosis, automatic modeling and tuning are examples of the software features that were used on this work. In following sections, the results and the methodology applied will be presented. 3.1 Oscillation detection The first step is to detect and to group the main oscillation cycles making use of the density spectral analysis. Table 1 shows the three most important cycles of a group of control loops of flotation area. Table 1: Oscillation cycles and diagnoses generated by the software. Control Loops Description Period (sec) Power (%) Oscillatio n (%) Osc - Valve Osc - Tuning 1 FIC13405 (1) Spager Air Flow 13405 862.9 63.06 100 0 0 30-2 FIC13408 (1) Spager Air Flow 13408 827.3 76.59 100 0 0 100 80 3 FIC13403 (1) Spager Air Flow 13403 811.6 74.5 100 0 0 100 527.5 4 FIC13406 (1) Spager Air Flow 13406 804.1 71.93 100 0 0 100 181.5 5 FIC13432-2 (1) Starch Flow System B 780 42.13 100 0 0 100 276.5 6 DIC13441 (2) Density BO13441 774.6 15.79 100 20 0 0 6381 7 PIC13402 (2) 690.6 37.22 100 100 0 0 4502 8 PIC13405 (1) 688.7 38.24 100 100 0 0 140 9 PIC13406 (2) 685.4 31.49 100 100 0 0 220 10 PIC13408 (2) 680.7 26.82 100 0 0 20 135 11 PIC13403 (2) 655.1 21.41 100 10 0 0-12 PIC13407 (2) 628.7 23.84 100 10 0 20-13 PIC13401 (2) 628 16.74 100 30 0 0 83 14 LIC13403 (1) Foam Level col 13403 512 54.42 100 90 0 0 1814 15 LIC13402 (1) Foam Level col 13402 494.6 50.4 100 0 100 0 2152 16 LIC13408 (1) Foam Level col 13408 491 60.1 100 10 0 0 2429 17 LIC13401 (2) Foam Level col 13401 475.5 22.23 100 90 0 0 2113 18 LIC13409 (1) Foam Level col 13409 457.8 66.78 100 0 0 0 2193 19 LIC13407 (1) Foam Level col 13407 449.2 68.4 100 100 0 0 1601 20 DIC13441 (2) Density BO13441 373.7 15.79 100 100 0 0 1741 21 LIC13443 (1) Level BO13443 337.7 53.84 100 100 0 0 1900 Osc Load RRT (sec) In rows 7 to 13 of the table, for example, we can see that the water pressure loops of the columns oscillate in a period near 10 minutes. This cycle can be verified visually in Figure 5. In three of them (PIC13402, PIC13405 and PIC13406) the cause of the oscillation has been associated to the actuator. The behavior of the PV (process variable) and MV (manipulated variable) signals, shown in Figure 6, can prove this diagnosis. The PV presents a behavior close to a square wave while MV looks like a triangular wave. The stiction presented in the valve can be quantified with specific tests that will indicate the necessity of maintenance. Regarding the other pressure loops, can they be oscillating due to the actuator problem identified? One way to answer this question is switching the loops with actuator problem in manual mode. Thus, the oscillation would stop and, in case of coupling, the same would happen with the pressure loops (at least in frequency with period of 10 minutes).
Figure 5: Oscillation in the pressure water loops flotation columns. Figure 6: PIC13402. Oscillation caused by stiction in the actuator. Many other groups of possible coupled loops can be detected using data showed in the table. It is important to mention that each group has to be analyzed in terms of the process to verify if the analysis makes sense. One way to get fast and good results is to analyze loops with actuators and tuning problems. The first ones should be submitted to more detailed tests with objective of validating the diagnoses and quantifying the problems. In case of loops with tuning-oscillation diagnoses, a retuning process should be performed. Based on a process model, new PID parameters should be calculated in order to make the controller follow the set-point and reject disturbances without causing oscillations. Tuning-oscillation in LIC13402: The oscillation analyses, showed in Table 1, points to a case of osculation caused by inadequate tuning in loop LIC13402. Figure 7 shows the temporal graphic of this loop.
Figure 7: LIC13402 Oscillation due to tuning. Figura 8: LIC13402 Set-point response. From the historical database, a set-point change moment was selected in order to get the process model. Figure 8 shows the data used in the tuning of the controller. Observing the trends one can see that it refers to an integrator process. The level decreases linearly when the controller output is zero and stabilizes right after the output returns to its last value. Figure 9: LIC13402 Model and tune parameters. Figure 9A shows the mathematic model obtained for the process. The validation was performed and we can see that the model fitted well the real data (Figure 9B). By means of this model, a new adjust for the controller was proposed (Figure 9C) objecting a no-oscillation control. Table 1 shows that the main oscillation cycle of LIC13402 is approximately 302 seconds. It corresponds to four times the dead time (0.78 minutes) verified in modeling.
Interacting loops: Another predictable coupling occurs between the loops DIC13441, density control of the feed flotation tank, and LIC13443, level control of the tank (see Table 1, lines 5 and 6). One possible cause of oscillation of these loops is what is named as interacting loops. One can see that they have almost the same RRTs. It means that the control of one affects directly the other one control, and vice-versa. A good practice to avoid that the loops fight against each other is to set their speed, measured by RRT, with a factor of 3, during the tuning work. 4 CONCLUSIONS The use of computational tools is essential to make possible this kind of work. Using spectral analyses tools, essentially in plants with a huge amount of control loops, is possible to get in real time the groups of coupled control loops and the cause of oscillation of each one. Through the use of this data, the maintenance team can get the relation of actuators that should be verified and the relation of loops that should be tuned. The result is a work that impacts directly in the cause of the variability, reducing it in a fast and efficient way.
REFERENCES [1] Ruel, M., Gerry, J. Quebec quandary solved by Fourier transform. Intech, 45: 8, 53-55, 1998. [2] Ruel, M. Tools to troubleshoot processes. ISA EXPO 2004, Houston, TX. [3] Shinskey, F.G. Process Control System, s. McGraw-Hill, 1996. cap.2 [4] PidTuner e PlantTriage Manual Expertune, 2005 www.expertune.com [5] Fonseca, M. O., Seixas, C., Torres, B. S. (2004). Avaliação de Desempenho e Auditoria de Malhas de Controle, Revista Intech Brasil, no 63, págs. 32 a 35. [6] Torres, B. S., Fonseca, M. O., Passos, L. F., Faria, D. C. (2004a). Avaliação de desempenho, diagnóstico automático e sintonia de malhas de controle auxiliados por software dedicado, Revista Controle & Instrumentação, Ano 10, Número 98, Novembro, Págs. 69-75. ABOUT THE AUTHORS Lúcio Dias Passos ATAN Sistemas de Automação Afonso Pena Av., 4001 9º. Floor Funcionários 30130-008 Belo Horizonte MG Phone: (31) 3261-8880 Fax: (31) 3261-8900 E-mail: lucio.passos@atan.com.br Bernardo Soares Torres ATAN Sistemas de Automação Afonso Pena Av., 4001 9º. Floor Funcionários 30130-008 Belo Horizonte MG Phone: (31) 3261-8870 / 8880 Fax: (31) 3261-8900 E-mail: bernardo.torres@atan.com.br Vicentino José Pinheiro Rodrigues Companhia Vale do Rio Doce. Mina de Conceição,Serra do Esmeril s/n. 35900-000 Itabira MG Phone: (31) 3839-5442 E-mail: vicentino.rodrigues@cvrd.com.br