A Disturbance Observer Enhanced Composite Cascade Control with Experimental Studies

Submission to International Journal of Control, Automation, and Systems 1 A Disturbance Observer Enhanced Composite Cascade Control with Experimental Studies Xisong Chen, Juan Li, Jun Yang, Shihua Li Abstract: The presence of strong disturbances usually cause great performance degradation of industrial process control systems. A disturbance observer (DOB) enhanced composite cascade control consisting of model predictive control (), proportional-integral-derivative (PID) control, and disturbance observer is proposed in this paper. DOB is employed here to estimate the severe disturbances and the estimation is applied for feed-forward compensation, forming a composite control together with. To evaluate the efficiency and validity of the proposed control structure, simulation as well as experimental studies have been carried out for a level tank process which represents a typical first-order plus dead-time (FODT) industry process. Both the simulation and experimental results show that the proposed composite control method significantly improves the disturbance attenuation property of the scheme in controlling such a typical industrial process. Keywords: Disturbance observer; Composite cascade control; Model predictive control; Experimental studies. 1. INTRODUCTION It is well known that model predictive control (), which is proposed by [1], is recognized as one of the most popular advanced control methods [2], especially in the field of industrial process control systems [3 5]. The potential reason of this fact may lie in that has several benefits, including [6] the underlying idea is straightforward to understand, extension to multivariable plants with almost no modification, and advantage in dealing with difficult loops such as those containing long time delays, etc. However, disturbances extensively exist in practical control systems, which significantly affect both the transient and steady-state performance of the engineering systems. As pointed out by [7], the feedback-based controllers generally demonstrate limited control performance in the presence of strong disturbance. The reason is that these controllers can not react directly and promptly enough to reject the disturbances, although they can finally suppress the disturbances through feedback regulation in a relatively slow way. This may cause a degradation of the This work was supported in part by Key technology support program of Jiangsu Province under Grant BE2012012, Graduate Innovation Program of Jiangsu Province under Grant CX10B_077Z, and New Century Excellent Talents in University under Grant NCET-10-0328. The authors are with School of Automation, Southeast University, Key Laboratory of Measurement and Control of CSE, Ministry of Education, Nanjing 210096, P.R.China. Corresponding author. Tel: +86-25-83793785; fax: +86-25-57712719. (e-mail: junyang8402@gmail.com). closed-loop control performance when subject to strong external disturbances. To this end, development of active disturbance rejection approaches is of great importance from the viewpoint of improving control performance. Feed-forward compensation control is known as an effective way to counteract the disturbances provided that they can be measured. However, it is usually hard or even impossible to measure the disturbances in many process systems, which motivates the disturbance estimation technique. Disturbance observer (DOB), which was firstly proposed by Ohnishi [8], provides a feasible approach to estimate disturbances and has been widely applied in various practical engineering systems, such as mechanical control systems [9 13], flight control systems [14 16] and many other general systems [17, 18]. The prevalence and the successful industrial applications of DOB based control lie in its powerful ability to reject and compensate disturbances and plant uncertainties [19]. Although DOB based control has achieved plenty of elegant results in both control theory and applications, it mainly has its roots in mechanical engineering societies. In recent years, DOB based control has become one of the hot topics in process control fields [20 22]. However, to the best of the authors knowledge, we can only find theoretical or stimulational results of DOB based control strategies in process control fields. Until now few experimental results have been reported in this fields, let alone industrial engineering applications. This paper aims to develop a disturbance observer enhanced model predictive control method to improve the disturbance rejection ability of a typical industrial process control system with

2 Submission to International Journal of Control, Automation, and Systems experimental results. In the DOB enhanced control structure, is designed to generate appropriate control actions so as to realize desired setpoint tracking response, while the DOB is separately designed to for disturbance estimation and compensation. In addition, to achieve a faster response of the closedloop system, a cascade composite control scheme is implemented to control a practical level tank which may be subject to severe disturbances. In such a composite control structure, the model predictive control serves as an outer-loop feedback controller, the PID control serves as an inner-loop feedback controller, and the DOB based control serves as an feed-forward compensator. Both the simulation and experimental studies have been carried out to show the effectiveness and feasibility of the proposed method. For the purpose of comparison, the based cascade control is also employed here. The comparison study results show that the proposed control method exhibits a promising ability in enhancing the disturbance rejection performance of such process system in the presence of strong disturbances. The rest of the paper is organized as follows. In Section 2, the control principle of the proposed method is addressed. Application of the proposed method to a level tank is investigated in Section 3. Simulation as well as experimental results and analysis are given in Section 4. The conclusions are finally given in Section 5. 2. DISTURBANCE OBSERVER ENHANCED MODEL PREDICTIVE CONTROL Since most of the process control systems can be modeled as first-order plus dead-time (FODT) or second-order plus dead-time (SODT) processes, the following model is considered to represent the general process systems with Y (s) = G p (s)u(s) + D ex (s), (1) G p (s) = g(s)e θs, (2) D ex (s) = m i=1 G di (s)d i (s), (3) where U(s) the manipulated variable, Y (s) the controlled variable, D i (s)(i = 1,...,m) the ith external disturbances, D ex (s) the effects of external disturbances on Y (s), G p (s) the model of the process channel, g(s) the minimum-phase part of G p (s), and G di (s)(i = 1,...,m) the model of ith disturbance channel. The nominal model G n (s) can also be represented as a product of a minimum-phase part g n (s) and a dead-time part e θ ns, i.e., G n (s) = g n (s)e θ ns. (4) 2.1. Model Predictive Control The process dynamic of system (4) can be represented as ŷ(t) = k=1 A(k) u(t k), u(t) = u(t) u(t 1), where u(t) the manipulated variable, ŷ(t) the output under the actions of u(t k)(k = 1,..., ) and A(k) is the dynamic matrix formed from the unit step response coefficients. According to (5), the ith step ahead prediction of the output with the prediction correction term is stated as ŷ(t + i) = i k=1 k=1 ξ (t) = y(t) ŷ(t), A(k) u(t + i k)+ A(k + i) u(t k) + ξ (t), where y(t) is the real time output, ξ (t) represents the prediction correction term. In (6), u(t + i k)(k = 1,...,i) denotes the future manipulated variable moves which is achieved by solving the following optimization problem P min J = u(t)... u(t+m 1) [e T (t + j)w e e(t + j)]+ j=1 M 1 j=0 e(t + j) = ŷ(t + j) r(t + j), [u T (t + j)w u u(t + j)], where P and M represent the prediction horizon and the control horizon, respectively, e(t + j) is the prediction error, r(t + j) is the desired reference trajectory, W e and W u represent the error weighting matrix and input weighting matrix, respectively. Only the first move is applied to the plant and this step is repeated for the next sampling instance. The choice of parameters prediction horizon (P), control horizon (M), error weighting matrix W e, input weighting matrix W u and sampling time T s have a profound effect on the control performance of the algorithms, such as stability and robustness. The general tuning guidelines of parameters have been widely discussed and analyzed in many literatures. The readers can refer to Refs. [23], [24] and [25] for details. 2.2. Disturbance Observer Enhanced Model Predictive Control The block diagram of the proposed disturbance observer enhanced model predictive control scheme is shown in Fig. 1. R(s) represents the reference trajectory of the controlled variable. C(s) stands for the output of the controller. Here, D ex (s) is supposed to be low frequency one, i.e., d ex ( jw) is bounded in a low frequency domain 0 < ω < ω, where ω is a cut-off frequency. ˆD f (s) denotes the disturbance estimation. (5) (6) (7)

Submission to International Journal of Control, Automation, and Systems 3 R(s) D ( s G ( s ) 1 ) d1 D m (s) G dm (s) D ex (s) u( t) u( t 1) u( t) C (s) U (s) Y (s) s g( s) e min J u ( t ) u ( t M 1) ˆ ( s) D f Q( s) e ns Q( s) gn 1 s ( ) Disturbance Observer Fig 1: Block diagram of the disturbance observer enhanced model predictive control. According to Fig. 1, the output can be expressed as where Y (s) = G cy (s)c(s) + G dy (s)d ex (s), (8) g(s)e θs G cy (s) = 1 + Q(s)g 1 n (s)[g(s)e θs g n (s)e θns ], (9) G dy (s) = 1 Q(s)e θ ns 1 + Q(s)g 1 n (s)[g(s)e θs g n (s)e θ ns ]. (10) It can be followed from Eqs. (8)-(10) that the disturbance rejection property mainly depends on the design of the filter Q(s) in DOB. The relative degree of Q(s) should be no less than that of the nominal model G n (s). This design principal is to make sure that the control structure is realizable, i.e., Q(s)G 1 n (s) should be proper. If we select Q(s) as a low-pass filter with a steady-state gain of one, i.e., lim Q( jω) = 1, it can be obtained from (10) ω 0 that lim G dy ( jω) = 0. This means the low-frequency disturbances can be attenuated asymptotically. So here Q(s) ω 0 is selected as a first-order-low-pass filter with the steadystate gain of 1, which can be expressed as Q(s) = 1,λ > 0. (11) λs + 1 The static disturbance rejection ability of the DOB is analyzed as follows. According to Fig. 1, the output Y (s) can be represented as where Y (s) = g(s)e θs U(s) + D ex (s) = g n (s)e θns U(s) + D m (s) + D ex (s), (12) D m (s) = [g(s)e θs g n (s)e θ ns ]U(s), (13) denotes the internal disturbances caused by model uncertainties. Let the lumped disturbances consisting of the external disturbances D ex (s) and the internal disturbances D m (s) D l (s) = D m (s) + D ex (s), (14) then, it follows from (12) that the output can be represented by Y (s) = g n (s)e θ ns U(s) + D l (s). (15) As shown in Fig. 1, the control law is where U(s) = C(s) ˆD f (s), (16) ˆD f (s) = Q(s)g 1 n (s)y (s) Q(s)e θ ns U(s), (17) Substituting Eq. (15) into Eq. (17) yields ˆD f (s) = Q(s)g 1 n (s)d l (s), (18) Define D l as the error between the real value and the estimated value of the lumped disturbance, i.e., D l (s) = D l (s) g n (s)e θ ns ˆD f (s) = [1 Q(s)e θ ns ]D l (s), (19) According to the Final-value Theorem, one obtains form Eq. (19) that d l ( ) = lim d l (t) t = lim s D l (s) s 0 = lim[1 Q(s)e θns ] lim sd l (s) s 0 s 0 = lim[1 Q(s)e θns ] lim d l (t) s 0 t = lim[1 Q(s)e θns ]d l ( ), s 0 (20) Obviously, if we select the steady-state of Q(s) is 1, then one obtains from Eq. (20) that d l ( ) = 0. (21)

4 Submission to International Journal of Control, Automation, and Systems Fine effects can be achieved by tuning the parameters of the controller and the time constants λ of the filter Q(s) in DOB. It should be pointed out that the implementation of DOB is rather simple, thus the introduction of feed-forward compensation part does not increase much computational complexity. Remark 1: It can be concluded from the above analysis that the disturbance estimation accuracy depends on the selection of the filter parameter λ in Q(s). Actually, it follows from Eqs. (19) and (20) that the property of disturbance estimation is determined by the frequency characteristics of transfer function 1 Q(s)e θ n(s). The smaller the filter parameter λ is, the smaller the magnitude of transfer function 1 Q(s)e θ n(s) is. This implies that the error of disturbance estimation converges to a arbitrarily small area by choosing a sufficiently small parameter λ in filter Q(s). It is also report in [19] that for an uncertain linear minimum phase plant, if the nominal plant has been stabilized by feedback controller, the robustness of DOB against arbitrary large but bounded uncertainties can be achieved by choosing a sufficiently smaller filter constant λ in Q(s). Remark 2: Note that Eqs (8)-(21) is only a steady-state analysis. Thus, the disturbance is supposed to have a constant steady-state value. Actually, in the presence of step disturbance, the DOBC can quickly compensate the disturbance and achieve offset free performance, while in the presence of low-frequency time-varying but bounded external disturbances, it has been claimed by [19,26,27] (and also the references therein) that the disturbance estimation error can be forced to a very small region by appropriately tuning the time constant in the filter Q(s). 3. APPLICATION ON AN EXPERIMENTAL SYSTEM 3.1. System Modeling of the Level Tank The level tank control system is a typical and commonly used industry process, and the principal diagram of the level tank studied here is shown in Fig. 2. The controlled variable is the water level, and the manipulated variable is the input flow rate. Obviously, the overall mass balance equation is Q i ρ + Q d ρ Q o ρ = ρ dv dt, (22) where Q i is the input flow rate of the level tank, Q o is the output flow rate of the level tank; Q d is the disturbance flow, V is the capacity of the level tank and ρ is fluid density. Let H the level height of the liquid inside the level tank, and A the cross-sectional area of the level tank, we have V = AH, (23) So Eq. (22) can be rewritten as Q i + Q d Q o = A dh dt. (24) Qi A H Qd Fig 2: The abstract model of level tank system. For such a level tank, the relationship between the output flow rate Q o and the level height is R Q 0 Q o = H R, (25) where R is the pipe resistance. Substitution Eq. (25) for Eq. (24), we have AR dh dt + H = RQ i + RQ d. (26) It can be seen form Eq. (26) that this is the first-order system. The time delay is generally unavoidable due to the fluid transport delay through pipes or measurement sample delay. Making Laplace transformation for Eq. (26) and taking into account the inherent time delay, the process channel model G p (s) can be represented as G p (s) = H(s) Q i (s) = Re θs ARs + 1, (27) Let AR = T, R = K, Eq. (27) becomes G p (s) = H(s) Q i (s) = Ke θs T s + 1. (28) 3.2. Control Design and Implementation In order to obtain a more prompt and linear response, a local PID controller is employed to control the flow rate which leads to a cascade control scheme. The experimental devices of the level tank studied here are shown in Fig. 3. All the signals from or to the level tank system are intercollected through digital-to-analog or analog-to-digital interfaces in a supervisory control and data acquisition (SCADA) system which works in a hierarchical manner. DOB based strategy is programmed by the configuration software WinCC from Siemens on supervisory computer and final commands are carried out through programmable logic controller (PLC). The control command from PLC will change the opening of the valve from 0% to

Submission to International Journal of Control, Automation, and Systems 5 PLC Siemens S7-300 Supervisory Computer Outer loop for level tank WinCC DOB for Disturbance estimation Configuration Monitor Data analysis Graphs, etc I/O modules CPU 315-2DP Inner loop PID control Level height Flowrate Valve opening The Level Tank Fig 3: Hierarchy diagram of the composite level tank control system. Disturbances Level setpoint Flowrate setpoint Valve position Input flow rate PID Valve Process Level Disturbance estimation Flow measurement DOB Level transmitter Fig 4: Control structure of the level tank system via the proposed method.

6 Submission to International Journal of Control, Automation, and Systems 100%.The detailed control structure is shown in Fig. 4. In this strategy, the disturbance observer enhanced is known as the primary or outer-loop controller, while the PID controller is the secondary or inner-loop controller. From Fig. 4, we can see that the disturbance directly affects the primary output (level). Note that the disturbance models are not necessarily required for the proposed method, thus only the process channel is modeled via step response test and represented as G n (s) = 9.98 11.965s + 1 e 1.8s. (29) The nominal values of the level tank system are: water level, 327 mm and input flow rate, 250 L/h. According to the discussions above, the filter in the DOB is selected as 1 Q(s) = 0.3s + 1, (30) The controller parameters of the proposed method of for the level tank system are selected as P = 8,M = 1,T s = 1/6 min,w e = I,W u = 1 The local PID controller parameters are designed as K p = 6.78,τ I = 2.6 min 4. SIMULATION AND EXPERIMENTAL STUDIES To demonstrate the benefits of the proposed method, the baseline cascade control method consisting of an outerloop and an inner-loop PID controller is employed here for the purpose of comparison. The performance indices including peak overshoot ratio (POR), settling time and integral of absolute error (IAE) are introduced to evaluate setpoint tracking performance of the closed-loop system. 4.1. Simulation Results and Analysis During the simulation studies, it is supposed that the disturbance (e.g., another input flow rate variation) is imposed on the input channel. Actually, the disturbance appears as d(t) = 0 L/h for 0 t < 50, 150 L/h for 50 t < 120, 0 L/h for t 120. (31) In this case, the tank level and input flow rate under the control of both and the proposed methods are shown in Figs. 5 and 6, respectively. The corresponding performance indices are listed in Table 1. It can be observed from Fig. 5 and Table 1 that the proposed method significantly improves the disturbance rejection performance as compared with the baseline based cascade control method, including a much smaller overshoot, a shorter settling time, and a smaller value of IAE. Table 1: The simulation performance indices Method DOB- POR(%) 0.29 0.12 Settling time 123 80 IAE 16079 1485.4 Level,mm 450 400 350 300 250 DOB 200 0 40 80 120 160 200 Time,min Fig 5: Simulation tank level response under the (broken line) and the proposed method (solid line). Flow rate,l/h 300 250 200 150 100 DOB 50 0 40 80 120 160 200 Time,min Fig 6: Simulation input flow rate under the (broken line) and the proposed method (solid line). 4.2. Experimental Results and Analysis To evaluate the practicality of the proposed method, experimental studies are also implemented in this paper. The disturbance added here is different but quite similar to that of the simulation case. In fact, another input flow rate variation is imposed on the system by setting the valve from close to open, and then close finally. Since the flow rate variation is large, it is supposed that strong disturbances occur here. The experimental data of the tank level and the input flow rate under both the and the proposed methods

Submission to International Journal of Control, Automation, and Systems 7 are shown in Figs. 7 and 8, respectively. The corresponding performance indices are listed in Table 2. Table 2: The experimental performance indices Method DOB- POR(%) 0.33 0.28 Settling time 540 190 IAE 13006 5511.9 Level,mm 440 420 400 380 360 340 320 DOB 300 0 100 200 300 400 500 600 700 Time,sec Fig 7: Experimental tank level response under the (broken line) and the proposed method (solid line). Flow rate,l/h 400 350 300 250 200 150 100 50 DOB 0 0 100 200 300 400 500 600 700 Time,sec Fig 8: Experimental input flow rate under the (broken line) and the proposed method (solid line). Also shown in Fig. 7 and Table 2, the overshoot under the proposed method is 28%, while it is 33% under the method. The settling time under the proposed method is about 190 seconds, while it is 540 seconds under the method. The IAE under the DOB- method is much smaller than that under without DOB. In general, the proposed method achieves much better disturbance rejection property than that of the method in both steady state and transient state. To this end, it can be said that the proposed method provides an effective way in improving disturbance rejection performance for such kind of process control systems. 5. CONCLUSION A composite cascade anti-disturbance control consisting of model predictive control, PID control, and disturbance observer has been proposed to control the first-order plus time-delay process. The has advantages in handling dead-time processes due to its prediction mechanism. DOB has been used to estimate the disturbance and the estimation has been used for feed-forward compensation design to reject disturbance. Such disturbance observer enhanced model predictive control method has been applied to control the level tank which may be subject to strong disturbances. Both simulation and experimental studies have been carried out, and the results have demonstrated that the proposed method exhibits excellent disturbance rejection performance, such as a smaller overshoot, a shorter settling time and a smaller value of IAE. REFERENCES [1] C. R. Cutler and D. J. Ramaker, Dynamic matrix control a computer control algorithm, Proc. Joint Automatic Control Conference, San Francisco, CA, Paper WP5-B, 1980. [2] W. H. Chen, Stability analysis of classic finite horizon model predictive control, International Journal Control, Automatic Systems., vol. 8, no. 2, pp. 187-197, April 2010. [3] J. B. Rawlings, Tutorial overview of model predictive control, IEEE Control System Magazine, vol. 20, no. 3, pp. 38-52, June 2000. [4] J. Prakash and R. Senthil, Design of observer based nonlinear model predictive controller for a continuous stirred tank reactor, Journal of Process Control, vol. 18, no. 5, pp. 504-514, 2008. [5] J. Prakash, S. C. Patwardhan and S. L. Shah, State estimation and nonlinear predictive control of autonomous hybrid system using derivative free state estimators, Journal of Process Control, vol. 20, no. 7, pp. 787-799, August 2010. [6] J. M. Maciejowski, Predictive Control: with Constraints, Prentice Hall, London, 2001. [7] X. S. Chen, J. Yang, S. H. Li and Q. Li, Disturbance observer based multi-variable control of ball mill grinding circuits. Journal of Process Control, vol. 19, no. 7, pp. 1205-1213, February 2009. [8] K. Ohnishi, M. Nakao, K. Ohnishi and K. Miyachi, Microprocessor-controlled DC motor for loadinsensitive position servo system, IEEE Trans. on

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