On Tuning and Practical Implementation of Active Disturbance

Article pubs.acs.org/IECR

On Tuning and Practical Implementation of Active Disturbance Rejection Controller: A Case Study from a Regenerative Heater in a 1000 MW Power Plant Li Sun,† Donghai Li,† Kangtao Hu,*,‡ Kwang Y. Lee,§ and Fengping Pan‡ †

The State Key Lab of Power Systems, Department of Thermal Engineering, Tsinghua University, Beijing 100084, PR China Guangdong Electric Power Research Institute, China Southern Power Grid Co. Ltd., Guangzhou 510030, PR China § Department of Electrical and Computer Engineering, Baylor University, Waco, Texas 76798-7356, United States ‡

S Supporting Information *

ABSTRACT: Active disturbance rejection controller (ADRC) is emerging as a promising approach to deal with uncertainties, which has received many practical applications in motion controls. This paper discusses the issues that should be taken into account when applying ADRC in process industry. First, the strategies of bumpless transfer and anti-windup are introduced to make ADRC applicable for continuous production processes. Second, an automatic tuning tool, based on robust loop shaping, is developed to obtain a group of reasonable parameters that can guarantee the system safety when ADRC is put in loop. For robustness concerns, the maximum sensitivity function is introduced in tuning the bandwidth of the extended state observer (ESO). Third, a quantitative retuning strategy is introduced to avoid the proportional kick in set-point tracking. The simulation and laboratory experiments confirm the effectiveness of the proposed strategies. Finally, it is attempted to apply the ADRC controller to a regenerative heater in an inservice 1000 MW power plant. The field test well demonstrates the virtues of ADRC and indicates promising prospects for ADRC in industrial applications.

1. INTRODUCTION Despite the success of the enormous advanced control theory, the proportional-integral-derivative (PID) controller by far still dominates the process industry.1 In a recent survey2 of more than 100 boiler-turbine units in Guangdong Province, China, 98.1% of the controllers are of PID type, 94.4% of which are in fact PI because derivative action may bring chattering to the manipulated variables (MV). The awkward gap between the booming theory and fogyish practice may be attributed to the following: (i) the PID controller can give good enough results in many cases with rough requirements; (ii) the implementation is complex for many advanced controls, for example, model predictive control, intelligent control, and nonlinear differential geometric control. The computational complexity makes it difficult to realize the advanced methods via existing function blocks in the distributed control system (DCS), which is widely used in process control. Therefore, in most cases, an additional high-performance computer is required to calculate the advanced control signals, which should be communicated with the DCS in real time.3 However, such treatment is usually at odds with the practice of field engineers due to the additional cost and the potential risks in case of communication failure. Moreover, it is challenging to ensure the long-term synchronization between the DCS and the additional computer. In the recent decade, active disturbance rejection control (ADRC),4 which was developed from PID, has emerged as a promising control method that well balances the efficiency and © 2016 American Chemical Society

complexity. It treats the internal unmodeled dynamics and external unknown disturbances as a lumped disturbance, which is estimated by the extended state observer (ESO) and then rejected in real time. Therefore, the uncertain plant is approximately compensated as a canonical form, based on which a simple feedback control law is determined to achieve a desired tracking performance despite the modeling uncertainties. It should be addressed that, from a theoretical point of view, ADRC is particularly suitable for process control in that (i) disturbance rejection (also known as regulation) is the primary concern in process industry,5,6 (ii) modeling uncertainty is significant due to the difficulty in accurately describing a complex industrial process, and (iii) in the cases where setpoint tracking is necessary, ADRC can produce a robust tracking performance as desired. In current practices, the efficacy of ADRC has been exemplified by many experimental applications in motion controls.7−11 In process control, there have been many simulation studies12−15 and laboratory water tank experiments16,17 to show the potential of ADRC. Received: Revised: Accepted: Published: 6686

April 1, 2016 May 24, 2016 May 26, 2016 May 26, 2016 DOI: 10.1021/acs.iecr.6b01249 Ind. Eng. Chem. Res. 2016, 55, 6686−6695

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Industrial & Engineering Chemistry Research

f as an extended state x2, then eq 2 can be expressed in a statespace form,

To implement ADRC in practical industry, some particular requirements arose in that many chemical plants are required to work in continuous duty. The implementation of the advanced controllers should not interrupt the productive process. Therefore, for long-term reliability, it requires that (i) the original PID controller should be transferred to ADRC in a bumpless manner, (ii) the control performance of the initial controller parameters should be acceptable and at least stable, and (iii) it should be friendly for the field engineers to retune the parameters based on their preferences. On the basis of the conventional frequency response, the above requirements are fulfilled theoretically, making ADRC compatible with the circumstances of process control. It should be pointed out that the proposed retuning strategy overturns the traditional view that is a common sense in motion controls. Inherited from the PID controller, the merit of simplicity features ADRC as a friendly method in engineering. First, the first-order ADRC controller can be deemed as a modified version of the PI controller by replacing the integrator with ESO.17 Thus, the control algorithm of ADRC can be readily configured using the function blocks in the DCS, requiring no additional hardware support and obtaining stronger reliability for long-term operation. Second, the physical meanings of the ADRC parameters are even more explicit than those of PID, leading to intuitive automatic tuning and quantitative retuning strategies. The main contribution of this paper is to test the feasibility and effectiveness of ADRC via implementation in a large-scale plant. The experimental results agree well with the theoretic predictions, demonstrating the promising prospect for ADRC in process control. The remainder of this paper is organized as follows: Section 2 briefly reviews the fundamentals of ADRC and addresses the problems of bumpless transfer and anti-windup. An automatic tuning tool is developed in section 3 as well as a quantitative retuning strategy. Section 4 demonstrates the efficiency of the proposed methods via laboratory experiment. After that, the ADRC controller is implemented in a field application in section 5. Finally, the conclusions and future work are pointed out in section 6.

⎧ ⎡ x1̇ ⎤ ⎪⎢ ⎥ = ⎪ ⎣ x 2̇ ⎦ ⎨ ⎪ ⎪ y = [1 ⎩

(3)

⎡ z1̇ ⎤ ⎡−β1 1 ⎤⎡ z1 ⎤ ⎡b0 β1 ⎤⎡ u ⎤ ⎥⎢ ⎥ ⎥⎢ ⎥ + ⎢ ⎢ ⎥=⎢ ⎣ z 2̇ ⎦ ⎢⎣−β2 0 ⎥⎦⎣ z 2 ⎦ ⎢⎣ 0 β2 ⎥⎦⎣ y ⎦

(4)

The convergence of ESO is proven provided that f ̇ is bounded. The number of the observer parameters can be reduced to one in terms of an observer bandwidth ωo,21 20

β1 = 2ωo ,

β2 = ωo 2

(5)

By compensating the estimation of the “total disturbance” in the inner-loop, as illustrated in Figure 1, u − z2 u= 0 b0 (6) an enhanced plant, from u0 to y, can be obtained, ⎛ u − z2 ⎞ ⎛u − y ̇ = f + b0⎜ 0 ⎟ ≈ f + b0⎜ 0 ⎝ b0 ⎠ ⎝ b0

f⎞ ⎟ = u0 ⎠

(7)

which can be approximately deemed as a simple integral process.

Figure 1. Principle schematic of ADRC.

Therefore, it is easy to control the enhanced plant (eq 7) by a proportional error feedback law, u0 = k p(r − y)

(8)

where r is set-point (SP). Based on eqs 7 and 8, we have the following closed-loop transfer function, Gcl(s) =

(1)

kp y(s) 1 = = r (s ) s + kp Tds + 1

(9)

where Td = 1/kp is the desired time constant of the tracking performance in response to a step change in set point. 2.2. Practical Issues of ADRC Application in DCS. The premises of implementing the above principles in industry are discussed in this section. The first problem is when to switch PID to ADRC and how to determine the initial values of the states z1 and z2. If the initial values of the states are set unreasonably, a considerably long time is needed for the convergence of ESO, that is, z1 tracking x1 and z2 tracking x2. During the convergence transient, there would appear a “peaking value” phenomenon.22

where d is the external disturbance, g represents the unknown model, and b is a critical gain, representing the power with which the controller output u can influence the process variable (PV) y. Since b is uncertain and may be time-varying, the plant eq 1 is rewritten as

y ̇ = f + b0u

⎡ x1 ⎤ 0]⎢ ⎥ ⎣ x2 ⎦

for which an extended state observer (ESO) can be designed as

2. ACTIVE DISTURBANCE REJECTION CONTROL 2.1. A Brief Overview of the Theory. ADRC was originally proposed for the general nth order process, where an nth order ADRC is used.18 But accurate model order is usually unavailable in process control. Moreover, it is cumbersome to realize the high-order controller by the simple modules in DCS. Therefore, a low-order ADRC controller is usually preferred in practice.19 For simplicity purposes, an uncertain system is first reorganized in a first-order form, y ̇ = g (t , y , y ̈ , ..., d) + bu

⎡ 0 1 ⎤⎡ x1 ⎤ ⎡b0 ⎤ ⎡0⎤ ⎢⎣ ⎥⎦⎢⎣ x ⎥⎦ + ⎢ ⎥u + ⎢⎣ ⎥⎦f ̇ 0 0 1 ⎣0 ⎦ 2

(2)

where b0 is an approximation of b and f = g + (b − b0)u is called “total disturbance”, consisting of the unknown external disturbances and internal dynamics. Denote y = x1 and consider 6687

DOI: 10.1021/acs.iecr.6b01249 Ind. Eng. Chem. Res. 2016, 55, 6686−6695

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Evidently, the parameter b0 can be directly calculated from a given model. And it follows from eq 9 that kp can be simply determined based on the tracking requirement, which is usually accessible in the relevant Industry Standards. The only concern is the tuning of ωo, which should be determined based on trade-off between the performance and robustness. In frequency domain, the state space description (eq 4) of ESO can be transformed as

To avoid the abrupt change and the potential risk, it is reasonable to switch the controllers when the process is almost running at a steady state, that is, ẏ = 0. Therefore, it follows from eq 2 that, in steady state, the initial values of the ESO states can be accurately determined as z1 = y ,

z 2 = f = −b0u

(10)

Since the ESO (eq 4) can be realized by the DCS integrator blocks, which can work either in the normal calculation mode or in the tracking mode, the initial values of the PID and ADRC controllers can be set as follows: • In manual mode or PID automation mode, the integrator outputs of z1 and z2 should track y and −b0u, respectively. • In manual mode or ADRC automation mode, the output of the PID block should track the manipulated variable (MV), u. On the condition of the steady state, y ≈ r; thus it follows from eq 6 that the MV of a newly switched-in ADRC controller would remain constant. By doing so, the control modes now can be switched to each other simply by a one-click operation. Thus, the property of the bumpless transfer has been achieved conveniently. The second problem is to improve the control logics in case of actuator saturation. Actually the anti-windup design for ADRC is much simpler than that of PID. Recalling eq 4, the states of ESO are estimated based on the real-time MV and PV. Therefore, to guarantee the correctness of the ESO inputs, it is natural to revise the linear control law (eq 6) as a nonlinear form ⎧ umin if (u0 − z 2)/b0 < umin ⎪ ⎪ u0 − z 2 if umin < (u0 − z 2)/b0 < umax u=⎨ ⎪ b0 ⎪ if (u0 − z 2)/b0 > umax ⎩ umax

⎡ b0s 2ωos + ωo 2 ⎤ ⎢ 2 ⎥ 2 2 ⎡ z1(s) ⎤ ⎢ s + 2ωos + ωo s + 2ωo1s + ωo 2 ⎥⎡ u(s) ⎤ ⎢ ⎥=⎢ ⎥ ⎥⎢ ⎢⎣ z 2(s)⎥⎦ ⎢ −ωo 2b0 ωo 2s ⎥⎢⎣ y(s)⎥⎦ ⎢ 2 2 2 2 ⎥ ⎣ s + 2ωos + ωo s + 2ωos + ωo ⎦ (12)

Thus, by transfer function transformation, the accurate characteristics of the enhanced plant can be expressed as G EP(s) =

(s + ωo)2 P y(s) 1 = u 0 (s ) s (b0s + 2b0ωo + ωo 2P)

(13)

where P is the process model. Moreover, with tedious derivations, the control structure in Figure 1 can be equivalently transformed to the structure in Figure 3.

Figure 3. Two-degrees-of-freedom control structure of ADRC.

It is seen that ADRC is essentially a two-degrees-of-freedom (2-DOF) control method, where the feedback controller and set-point prefilter are, respectively,

(11)

which can be easily configured via the DCS limit block, shown in Figure 2. By constraining the inputs, ESO will always work correctly and the integral saturation for z1 and z2 is thus avoided.

GC(s) =

G F (s ) =

k ps 2 + (ωo 2 + 2k pωo)s + k pωo 2 b0s(s + 2ωo)

(14)

k p(s + ωo)2 k ps 2 + (ωo 2 + 2k pωo)s + k pωo 2

(15)

It should be pointed out that the conventional 2-DOF control methods usually involve two independent design tasks for GC(s) and GF(s) while, in ADRC, they are designed in a unified manner. A common index that is used to constrain the robustness of the process control system is the maximum sensitivity f unction, which is defined as

Figure 2. Anti-windup design of ADRC.

3. AUTOMATIC TUNING AND RETUNING Besides the previous preliminary works, a more important work is to determine a group of reasonable values that can guarantee an acceptable initial performance. 3.1. Automatic Tuning of ADRC Based on Robust Loop Shaping. In the previous work,17 we have developed an interactive tuning tool that was used in a trial and error way. In this paper, based on the nominal model, the tool will be upgraded to tune the parameters automatically to achieve desired performance and robustness.

MS = ∥S(s)∥∞ =

1 1 + L (s )

∞

(16)

where L(s) = GC(s)P(s) is the loop transfer function. A smaller MS corresponds to a better robustness, and reasonable range is 1.4 < MS < 2.0 for most industrial plants.23 It follows from eq 13 that a larger ωo is preferred to force the behavior of the enforced plant closer to the integrator, at least in low frequencies. However, in general cases in the presence of time delay or model order mismatch, a larger ωo tends to bring 6688


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Figure 4. An automatic tuning tool for ADRC (accessible via Supporting Information).

a bigger MS and thus poorer robustness. Actually, the MS contours in the complex plane are circles centered at (−1, j0). And the robustness constraints can be satisfied by shaping the Nyquist plot of the loop transfer function L(s) outside the MS contours. Thus, the parameter ωo can be solely determined based on a prescribed MS. This is the so-called robust loop shaping method,23 which is illustrated through the following example, P=

53.5 e −s (1 + 1094s)(1 + s)

G UR (s) = k ps 2 + (2k pωo)s + k pωo 2 (b0 + Pk p)s 2 + (2b0ωo + Pωo 2 + 2Pk pωo)s + Pk pωo 2 (18)

Thus, the initial value of the control action in response to the step reference change can be determined, 1 u(0) = lim sR(s)G UR (s) = lim s G UR (s) s →∞ s →∞ s

(17)

(19)

Since P(∞) = 0 holds for most chemical processes, if not all, we have

For ease of tuning, an automatic tuning tool is developed based on MATLAB, as shown in Figure 4. The tool and the code files are accessible in the Supporting Information. All the ADRC parameters can be automatically tuned with given control objectives on performance and robustness. The parameter ωo is searched based on the bisection method to let the Nyquist plot of L(s) right be tangent to the contour of a given MS, as shown in the subplot titled “Robustness Constraints” of Figure 4. 3.2. Retuning. It is seen from Figure 4 that the resulting tracking performance is almost perfect in that PV coincides well with the desired tracking trajectory. However, an obvious disadvantage of this group of parameters is that MV has a sudden change at the beginning of the reference step response (at t = 100s in Figure 4). Such impact to the actuator should be avoided for safety and long-term reliability purposes. To this end, the transfer function from the reference to the process variable is derived,

u(0) =

kp b0

(20)

Remark 1: Most chemical processes are featured by their slow variation rate (usually at hour level), which corresponds to a significantly small b0 based on its physical meaning. It follows from eq 20 that a b0 that is far less than 1 will produce a big “proportional kick” at the beginning of the closed-loop step response. In motion controls, contrarily, b0 is usually much bigger than 1 due to the fast transient. The resulting “proportional kick” is not a significant problem and thus caught little attention in that field. To avoid the “proportional kick” while maintaining the performance, we analyze the transfer function from disturbance to PV 6689


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Industrial & Engineering Chemistry Research G YD(s) = (Pb0)s 2 + (2Pb0ωo)s (b0 + Pk p)s 2 + (2b0ωo + Pωo 2 + 2Pk pωo)s + Pk pωo 2 (21)

whose low-frequency characteristics can be approximated as G YD(s) =

Pb0 s ̷ + 2Pb0ωo (b0 + Pk p) s ̷2 + (2b0ωo + Pωo2 + 2Pk pωo) s ̷ + Pk pωo2

2b0 ≈ s= s 2 k pωo Pk pωo

s s→0

2Pb0ωo

(22)

Since the disturbances are mainly of low frequency in process industry, we have a great confidence to declare that Remark 2: the regulatory performances of the ADRC control system would be similar if the ratio between kp, ωo, and b0 is constant. It follows from eq 9 that kp is the dominant parameter for the tracking performance. Therefore, we can further claim that Remark 3: without compromises to the performances of tracking and disturbance rejection, the proportional kick u(0) can be reduced via increasing b0 and ωo by the same factor. Actually, it has been proven24 that the tuning parameter b0 belonging to b/b0 ∈ (0, 2) is permitted by the stability and convergence of ADRC, implying that b0 can be tuned arbitrarily large. Moreover, the transfer function from the high-frequency measurement noise to MV is derived as

Figure 5. Simulation results with retuned parameters (kp = 0.01).

G UN =

k ps 2 + (ωo 2 + 2k pωo)s + k pωo 2 (b0 + Pk p)s 2 + (2b0ωo + Pωo 2 + 2Pk pωo)s + Pk pωo 2

s →∞

=

kp b0

(23) Figure 6. Frequency responses of GYD(s) (kp = 0.01).

Obviously, the control system that has a smaller proportional kick, that is, a bigger b0, will be less sensitive to the measurement noise. Remark 4: In summary, for chemical processes with large time constants, the design principle for b0 is to increase the real value b by several times. Meanwhile, the bandwidth ωo should be increased by the same factor. It will not degrade the tracking and regulatory performances. The resulting benefits are (i) the initial proportional kick is avoided and (ii) the effects of the measurement noise are reduced. 3.3. Simulation Test. To confirm the feasibility of the above retuning strategy, simulations are carried out based on the model of eq 17. To maintain the tracking performance, kp is kept as 0.01, as tuned by the automatic tuning tool. To maintain the regulatory performance, b0 and ωo are increased simultaneously by the same (5 and 10 times) factor. A step disturbance is added to the system at t = 500 s. The simulation results are shown in Figures 5−7. It is confirmed in Figure 5 that the regulatory performances are almost the same for the original and retuned parameters, which is also validated by the frequency responses of the transfer function from disturbance to PV in Figure 6. For tracking performances, the settling times of the original and retuned parameters are almost the same. However, as seen from the inset of Figure 5, the initial proportional kick of the

Figure 7. Frequency responses of the sensitivity function S(s).

retuned parameters is significantly reduced with the compromise that the initial responses are slightly slower than that of the original parameters. 6690


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confirming the fine ability of the anti-windup strategy in section 2.2. 4.3. Experimental Test of Tuning and Retuning. The model of the water tank is identified as eq 17, based on which a group of initial parameters have been automatically determined in section 3.1, and two sets of retuned parameters are given in section 3.2. The performances of the initial and retuned parameters are shown as five stages in Figure 10. In the first stage of the experiment, the tracking and regulatory performances are satisfactory, while there exists obvious proportional kick in MV (see the ellipse mark A). In the second and third stages, the proportional kick is avoided while the performances are maintained with a gradually changing MV (see the ellipse mark B). Moreover, the control action is less sensitive to the measurement noise. To further discuss the parameters’ effects, ωo is solely increased to 0.5 based on the original parameters in the fourth stage. It is seen that the resulting tracking performance is almost identical to that of the initial parameters, as promised by the same kp, while the regulatory performance is significantly improved due to the bigger ωo. We further increase kp to 0.02 in the fifth stage. The resulting tracking performance is correspondingly accelerated. But there is no obvious improvement in disturbance rejection due to the physical limit on the pump motor. The control actions in the fourth and fifth stages are sensitive to the measurement noise. Evidently, the experimental results completely agree with the predictions of the analysis and simulation in sections 2 and 3.

Another merit of the retuned parameters is that the magnitudes of the sensitivity function S(s) in eq 16 are smaller than those of the original parameters in low frequencies, implying a better robustness against the modeling uncertainties.

4. LABORATORY EXPERIMENTS Prior to industrial implementation, a laboratory experiment is necessary to confirm the feasibility of method and the validity of the theoretic analysis and simulation results above. 4.1. Description of the Platform. Figure 8 shows the experimental platform, which is an industrial-scale water tank,

Figure 8. Experimental platform with a water tank and DCS.

5. A FIELD APPLICATION TO REGENERATER Motivated by the encouraging results of the analysis, simulation, and laboratory experiment, a field test is carried out as described in this section based on the automatic tuning and retuning strategy. 5.1. Process Description. ADRC is tested in a regenerator in a 1000 MW in-service power plant, as show in Figure 11. The regenerator is a surface-type heat exchanger that is used to heat the working fluid (tube side) by the high-temperature steam (shell side) extracted from the turbine. The process variable to be controlled is the level of the condensate, which should be maintained at a desired value. A higher or lower level than the set-point would deteriorate the heat exchange efficiency or even threaten the safety of the regenerating system. The manipulated variable is the #1 valve position that controls the condensate flux to the next regenerator. There are three major sources of disturbances in this process, the steam flux from the turbine, the working fluid flux, and the opening position of the #2 valve. Unlike the frequent disturbances from steam and working fluid, the #2 valve is usually closed if no emergency occurs. The control goals of the regenerator are listed as follows: • The primary goal is to regulate the condensate level as close to constant as possible in face of disturbances. • Set-point tracking is a less important goal, which is rarely required when starting or stopping the machine. The phenomenon of proportional kick should be avoided to protect the valve. Based on an open-loop step response, a transfer function from the #1 valve position to the level is identified as

consisting of a water tank, pump, monitor, and DCS hardware. The process variable is the water level and the manipulated variable is the rotating speed of the pump motor. The disturbance variable is the opening position of the outlet valve. The DCS used in this system is the SUPCON WebField ECS-100. The control logics are configured based on the control law and switch strategy in section 2, which is accessible in Supporting Information. 4.2. Experimental Test of Bumpless Transfer and Antiwindup. The test starts with a step set-point tracking using the PI controller. After reaching the new steady-state condition, the controller is switched from PI to ADRC smoothly, as shown in Figure 9. It is confirmed that the objective of bumpless transfer has been well fulfilled. The next three step tracking commands make MV stay at its upper and lower limits for some time,

G (s ) = − Figure 9. Experimental test of bumpless transfer and anti-windup. 6691

100 e − 2s (1 + 1200s)(1 + 3s)

(24)


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Figure 10. Experimental results for the initial and retuned parameters.

Figure 12. Results of the automatic tuning and simulation.

Figure 11. Illustration of the regenerator.

where the inertial constant 1200s represents the dynamics of the regenerator. The inertial constant 3s represents the dynamics of the actuator, which is also a feedback control system. The 2s represents all the delays in the control system. By omitting the negligible time delay, the model (eq 24) can be expressed as the form formulated in eq1, y ̇ = −2.99y ̈ − 8.31 × 10−4y + 0.0083u

(25)

5.2. Parameter Tuning and Simulation. By checking the operating discipline in power plant industry, the recommended tracking constant is 100s, which is set to be in accordance with the starting or stopping procedures of other facilities. The robustness level is again conservatively determined as 1.4. The tuning and simulation results are shown in Figure 12.

Figure 13. Comparative results of the original and retuned parameters.

It is seen that the performances of the automatically tuned parameters are satisfactory. To avoid the proportional kick in 6692


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point from 70 mm to 30 mm and finally to 500 mm. The resulting tracking performance of the ADRC controller is shown in Figure 14. It can be seen that the process variable agrees well with the desired tracking trajectory despite the modeling inaccuracies and frequent disturbances from the shell and tube sides. To test the regulatory performances, a ±10% disturbance of the opening position is arbitrarily added to the #2 valve. The comparison results of the ADRC and PI controller are shown in Figures 15 and 16. The parameters of PI controller are tuned by the experienced engineers, based on trial and error, with the goals to fulfill both requirements on disturbance rejection and set-point tracking. It should be pointed out that, when tuning PI, much effort was done to enhance its ability of disturbance rejection while maintaining the tracking performance close to the trajectory suggested by the operating discipline. However, compared with ADRC, the PI controller produces a much more sluggish regulatory response although the resulting tracking performance has already been tuned to be faster than expected. Moreover, the ADRC solution does not have proportional kick in set-point tracking while the PI controller does. 5.4. Discussion. The field test confirms the merits of ADRC in terms of the essential two-degrees of freedom (2DOF) nature. That is, the objectives of tracking and disturbance rejection can be decoupled and realized individually. Besides the 2-DOF nature, another advantage of ADRC is that it can arrange the control effort from the beginning stage to the later while keeping the tacking and regulatory performances almost unchanged.

Figure 14. Tracking performance of the ADRC controller.

MV, the parameters b0 and ωo are amplified by the same factor to −1 and 0.78, respectively. The comparison results are shown Figure 13. The disturbance rejection of the retuned parameters becomes a little sluggish, but the MS is reduced to 1.2, implying a better robustness. The set-point tracking is similar to that of the original parameters with a slower initial response but smaller settling time. Moreover, the initial sudden change does not appear in MV of the retuned parameters. 5.3. Field Test. Based on the preparatory work in section 2, we configured the control logics in the Symphony Plus DCS of ABB, which can be found in Supporting Information. Since the retuned parameters lead to a quite conservative robustness level, MS = 1.2, we have enough safety margin to implement the ADRC controller with the retuned parameters, kp = 0.01, b0= −1, ωo = 0.78. With the convincing materials above, the manager of the power plant agreed to online download the ADRC control logics with well-tuned parameters into the digital processing unit (DPU) of DCS. After bumpless transfer to ADRC, the experiment was carried out by changing the set-

6. CONCLUSION AND FUTURE WORK Aiming at implementing the ADRC controller in process control, this paper discusses the practical issues that should be taken into account in engineering. Besides the bumpless transfer and anti-windup design, the first contribution of this paper is to propose an automatic tuning strategy based on robust loop shaping. Second, a quantitative retuning strategy is given to avoid the proportional kick in set-point tracking. The theoretic analysis reveals the user-friendly virtue of ADRC, which is intuitive for understanding and ease of practice for field engineers. With confidence from the preliminary works,

Figure 15. Field test result of the ADRC controller (The time span is 33 min). 6693


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Figure 16. Field test of the PI controller (The time span is 60 min).

the ADRC is finally applied to the regenerator control in an inservice power plant. Although simple, the analysis, simulation, laboratory, and field experiments give mutual support to each other, confirming the feasibility of ADRC and the effectiveness of the proposed strategy on applying ADRC, and depicting a promising prospect of ADRC as an alternative in process industry.

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(6) Gao, Z. On the centrality of disturbance rejection in automatic control. ISA Trans. 2014, 53 (4), 850−857. (7) Tan, W.; Fu, C. Linear Active Disturbance Rejection Control: Analysis and Tuning via IMC. IEEE Trans. Ind. Electron. 2016, 63 (4), 2350−2359. (8) Li, S.; Li, J.; Mo, Y. Piezoelectric multi-mode vibration control for stiffened plate using ADRC-based acceleration compensation. IEEE Trans. Ind. Electron. 2014, 61 (12), 6892−6902. (9) Li, J.; Ren, H. P.; Zhong, Y. R. Robust Speed Control of Induction Motor Drives Using First-Order Auto-Disturbance Rejection Controllers. IEEE Trans. Ind. Appl. 2015, 51 (1), 712−720. (10) Chang, X.; Li, Y.; Zhang, W.; et al. Active disturbance rejection control for a flywheel energy storage system. IEEE Trans. Ind. Electron. 2015, 62 (2), 991−1001. (11) Wang, J.; Li, S.; Yang, J.; Wu, B.; Li, Q. Extended state observerbased sliding mode control for PWM-based DC−DC buck power converter systems with mismatched disturbances. IET Control Theory Appl. 2015, 9 (4), 579−586. (12) Li, D.; Li, Z.; Gao, Z.; Jin, Q. Active Disturbance RejectionBased High-Precision Temperature Control of a Semibatch Emulsion Polymerization Reactor. Ind. Eng. Chem. Res. 2014, 53 (8), 3210− 3221. (13) Huang, C. E.; Li, D.; Xue, Y. Active disturbance rejection control for the ALSTOM gasifier benchmark problem. Control Engineering Practice 2013, 21 (4), 556−564. (14) Yuan, G.; Du, J.; Yu, T. Performance Assessment of Power Plant Main Steam Temperature Control System based on ADRC Control. International Journal of Control and Automation 2015, 8 (1), 305−316. (15) Liang, G.; Li, W.; Li, Z. Control of superheated steam temperature in large-capacity generation units based on active disturbance rejection method and distributed control system. Control Engineering Practice 2013, 21 (3), 268−285. (16) Madonski, R.; Nowicki, M.; Herman, P. Application of active disturbance rejection controller to water supply system. In Proceedings of the 33rd Chinese Control Conference, Nanjing, China; Xu, S., et al., Eds.; IEEE: Piscataway, NJ, 2014 pp 4401−4405. (17) Sun, L.; Dong, J.; Li, D.; Lee, K. Y. A practical multivariable control approach based on inverted decoupling and decentralized active disturbance rejection control. Ind. Eng. Chem. Res. 2016, 55 (7), 2008−2019. (18) Huang, Y.; Xue, W. Active disturbance rejection control: methodology and theoretical analysis. ISA Trans. 2014, 53 (4), 963− 976. (19) Zhao, C.; Li, D. Control design for the SISO system with the unknown order and the unknown relative degree. ISA Trans. 2014, 53 (4), 858−872. (20) Zheng, Q.; Gao, L.; Gao, Z. On stability analysis of active disturbance rejection control for nonlinear time-varying plants with

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b01249. Configuration diagram of the ADRC control logics based on the ABB Distributed Control Systems (PDF) Configuration diagram of the ADRC control logics based on the SUPCON Distributed Control Systems (PDF) Execute file, code files, and instructions of the robust automatic tuning tool for ADRC (ZIP)

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AUTHOR INFORMATION

Corresponding Author

*Kangtao Hu. E-mail: [email protected]. Funding

This research was supported by National Natural Science Foundation of China (No. 51176086) and the S&T transfer project between Tsinghua University and Guangdong Electric Power Research Institute, China Southern Power Grid Co., Ltd. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Åström, K. J.; Hägglund, T. The future of PID control. Control engineering practice 2001, 9 (11), 1163−1175. (2) Sun, L.; Li, D.; Lee, K. Y. Optimal Disturbance Rejection for PI controller with Constraints on Relative Delay Margin. ISA Trans. 2016, DOI: 10.1016/j.isatra.2016.03.014. (3) Sun, L.; Li, D.; Lee, K. Y. Enhanced decentralized PI control for fluidized bed combustor via advanced disturbance observer. Control Engineering Practice 2015, 42, 128−139. (4) Han, J. From PID to active disturbance rejection control. IEEE Trans. Ind. Electron. 2009, 56 (3), 900−906. (5) Shinskey, F. G. Process control: as taught vs as practiced. Ind. Eng. Chem. Res. 2002, 41 (16), 3745−3750. 6694


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On Tuning and Practical Implementation of Active Disturbance

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