Abstract In order to make an accurate prediction of the greenhouse environment parameters, this paper proposes a controlling method for greenhouse prediction. Targeting that the former greenhouse model is not precise enough, and that the model parameters are difficult to determine, the paper firstly makes an analysis of the technical difficulties, and then proposes a prediction method based on dynamic matrix control. This method is structural simple, stable to control, and highly precise. It can accurately predict the greenhouse environment parameters through a combination of simulation, and then achieve the final goal of controlling those parameters effectively.

I. INTRODUCTION reenhouse technology is one of the major parts of the modern agricultural technology, and the core of the

greenhouse environmental system lies in modeling and controlling technology [1]. Greenhouse controlling technology has become a major advanced technology among developed countries in the 21st century, as it could help to utilize the agricultural resources wisely, improve agricultural production, reduce the production cost, protect the ecological environment, and improve the competitiveness of agricultural products in the international market.

As a more accurate greenhouse model is in need these days, the greenhouse controlling model needs to be further developed. However, the current PID control and fuzzy control from the classical control theory are not that precise and intelligent as required. Therefore, it is necessary to develop a new controlling strategy which is low-demanding for model, comprehensively qualified in controlling, and easy to compute online.

The predictive controlling method has succeeded in complex industrial process in recent years, which attracts much attention from the greenhouse environment control field [2][9]. In 2008, a switch-based greenhouse modeling and controlling method was proposed by G. Wu et al. This method is structurally simple, mould plough effective and stable in control [2]. In 2008, F. W. Long et al. designed the DMC PID algorithm in large time delay system, considering that the greenhouse environment controlling system is nonlinear, slowly-varying, long-time-delayed and

This work was supported in part by the National Natural Science Foundation of China (Grant, 61174088).

Z. T. Xu is with the China Agricultural University, Beijing, 100083, China (xurgkamp@163.com).

Z. Y. Yao and L. J. Chen is with the China Agricultural University, Beijing, 100083, China (y_zhiying@163.com, 455135092@qq.com).

S. F. Du is with the China Agricultural University, No. 17, Tsinghua East Road,Haidian District, 100083, China(phone:+86-135-2076-0485 13520760485@126.com).

multivariable coupling. The system combined cascade control structure and predictive control algorithm, with the conventional proportional regulator used in the inner circuit, and dynamic matrix control (DMC) in the outer. It maintained the strong robustness feature and tracking function of the predictive controlling method, and gave a good performance in anti-interference [3]. In 2011, M. Shen et al. put forward a predictive controlling method, which optimized the combined effect of greenhouse controlling system switch equipment. With the equipment combination unchanged in no less than the maximum of delayed time or time domain, rolling optimization and predictive control are laid in the combined equipment, which has greatly simplified the predictive controlling algorithm for the greenhouse controlling system, and alleviated the long-time delay problem of controlling system distribution [4]. R. B. Zhang et al. proposed an adaptive decoupling method based on dynamic matrix control in view of the strong coupling between temperature and relative humidity in the greenhouse simulation system in 2012 [5]. J. Vasquez et al. changed the control rules dynamically in embedded digital control systems in 2010 [6]. C. Rodriguez et al. did research on diurnal greenhouse temperature control with predictive control and online constrains mapping in 2010 [7]. A. Pawlowskia et al. make a practical approach for Generalized Predictive Control within an event-based framework in 2012, and the performance of the proposed control algorithm is first verified for a first-order plus delay process and afterwards it is evaluated by using a case study based on the greenhouse temperature control problem [8]. A. Ramirez-Arias, et al. improved the efficiency of greenhouse heating systems using model predictive control in 2005. They made a comparison of commercial and model based predictive control strategies aimed at optimizing efficiency of classical heating systems used in greenhouse temperature control [9].

Dynamic matrix control (DMC) is a predictive control algorithm, which is widely accepted by practical applications [10]. The algorithm is simple, and its controlling effect is good. Dynamic Matrix Control is widely used in industrial control, while less applied in the field of agricultural engineering. Considering the special nature of greenhouse control, the paper studies the use of Dynamic Matrix Control Algorithm for greenhouse control system, and develops a control algorithm that meets the greenhouse control system needs. The study uses a simple greenhouse temperature model, designs a model predictive controller based on the DMC, and then runs simulation validation using matlab. Validation results show that predictive control has strong robustness and performs well in tracking, and is applicable in greenhouse environment control. It can improve the existing

Greenhouse air temperature predictive control using the Dynamic Matrix Control

Z. T. Xu, Z. Y. Yao, L. J. Chen, and S. F. Du

G

2013 Fourth International Conference on Intelligent Control and Information Processing (ICICIP) June 9 11, 2013, Beijing, China

978-1-4673-6249-8/13/$31.00 2013 IEEE 349

greenhouse control algorithm and be consistent with the development of current greenhouse control technology.

II. DYNAMIC MATRIX CONTROL The state space method has always been limited in

performing analysis and design for controlling system since the emergence of the modern control theory, for the reason that the object of it does not have an accurate mathematical model, which then could only yield a less precise control.

Since the 1970s, the traditional method constraint has been broken, and low-model-requiring algorithm has been searched. Since the 1990s, intelligent control which does not depend on an accurate model of the object has been developed, such as neural networks control, fuzzy control, etc. However, due to computational complexity and poor real-time performance to various degrees, it is still not applicable in the practical complex greenhouse system.

Dynamic matrix control algorithm is based on the object-step-response prediction model. Commonly, DMC controller includes three parts: predictive model, rolling horizon optimization, feedback correction [10].The flow chart of dynamic matrix control is shown in Fig. 1. Since it has less model parameters, it has simplified the computing process of the controlling algorithm. Dynamic matrix control has been successfully applied in the industrial field [11], therefore it is necessary to explore its application in the greenhouse controlling system.

Fig. 1. The flow chart of DMC

A. Prediction Model Based on the step-response of the controlled plant, the

dynamic characteristic of the plant can be described by a series of dynamic coefficient a1, a2, , aN, which are values of the step response at each sampling instant T, 2T, , NT, where N is called time domain length of model.

The unit step response of a linear object stable value of the sampling is:

)(iTaai = i=1,2,,N (1)

At t = kT, if the control amount is no longer changes, the

output value of the system at the next timing of the N is:

)(~),2(~),1(~ 000 kNkykkykky +++ In control of the role of the increment u (k), the output of

the system can be predicted:

)()(~)(~ 01 kuakyky NN += (2) Where TN kNkykkyky ])(~...)1(~[)(~ 000 ++= is the output

prediction of the next N timing when t=kt without the control increment u (k). TN kNkykkyky ])(

~...)1(~[)(~ 111 ++= is the output prediction of the next N timing when t=kt with the control increment u (k). TNaaa ]...[ 1= is step response model vector, whose elements are N-step response coefficients describing the system dynamics. In the (2), the superscript ~ indicates prediction.

The predicted output of the system under the action of control increment u (k), ... u (k + M-1) in the next P instants at time t = kT is:

)()(~)(~ 0 kuAkyky MPPM += (3)

Where:

TkNkykkyky ])(~...)1(~[)(~ 000P ++= is the predicted output without control increment for future P instants at t=kT.

TMMM kNkykkyky ])(

~...)1(~[)(~P ++= is the predicted output with control increment u (k), ... u (k + M-1) for future P instants at t=kT.

=

+ 11

12

1

000

Mppp aaa

aaa

A

"#"##

""

is called dynamic matrix. Its

elements describe the dynamic characteristics of the system step response coefficients.

B. Rolling Horizon Optimization DMC is a predictive control algorithm with optimization.

Its aim is that the future outputs on the considered horizon should follow a determined reference signal. Its expression for such an objective function will be:

=

=

+

+++=

M

1

2

1

2

)1(

)](~)([)(min

jj

P

iMi

jkur

kikyikqkJ

(4)

Where, w (k + i) is the desired output value, P is called

optimization domain, M referred to as the control horizon, qi,

350

and ri are the weight coefficients. The optimal real-time control increment at k instants is:

))(~)(()()( 01 kykQARQAAku pp

TTM +=

(5) Where:

Tp Pkkk )]()...1([)( ++= ,

Q=diag(q1,,qP), R=diag(r1,,rM).

C. Feedback Correction Due to the plant-model mismatch, various uncertainties

such as the measurement noise, the unpredictable plant parameter variations, and the external load disturbance etc., the plant output inevitably deviates from the model output. So the closed loop control algorithm must be employed.

Let y(k+1) be actual output of the plant at k+1 instant, and e(k+1) is the error between the actual and predicted outputs of the system, then

)1(~)1()1( 1 kkykyke ++=+ (6)

The output error reflects the effects of the uncertainties on

the plant output. It can be used to adjust the future predicted outputs. When the weighting factor method is applied to the future predicted outputs, obtain

)1()(~)1(~ 1 ++=+ kHekYkY Ncor (7)

Where:

TN kNkykkykY )]|(~)...|1(~[)(

~111 ++=

Tcorcorcor kNkykkykY ])1(~...)11(~[)1(

~++++=+

TNhhH ]...[ 1=

At k+1 instant, the future time point of predicting the future outputs should be moved to k+2, ... , k+N+1. Thus, the elements of cor(k+1) need be shifted to obtain the initial predictive values at k+1 instant, i.e.,

)1(~)1(~ 0 +=+ kYSkY corC (8)

Where:

TC kNkykkykY )]1|1(~)...1|2(~[)1(

~000 +++++=+

=

1001000010

""##""

S .

Based on C0(k+1), the same optimization as the preceding section would be performed to get the u(k+1) at k+1 instant. It is so called rolling optimization strategy.

The form of feedback correction can be varied. Regardless of the form of correction, the optimization of dynamic matrix control is regarded to create the system based on the actual and try to make a more accurate prediction of the dynamic

behavior of the system in the optimization. Accordingly, the dynamic matrix control is not only based on the model, but also using the feedback information, so dynamic matrix control is a closed-loop control algorithms optimized.

In summary, the dynamic matrix control has distinctive characteristics as a new computer control algorithm.

III. SIMULATION IN THE GREENHOUSE CONTROL SYSTEM The most important aspects of the greenhouse predictive

control system is temperature control. The actual value of the greenhouse temperature is the controlled variable. Through the heating, refrigeration equipment, temperature is closer to the value of the system. The object is a first-order delay object lingering objects equation:

)/( kaseG s += (9)

Where k is the amount of greenhouse heat loss, W / m2; the

a is the greenhouse heat capacity, J / m2; the is the delay time, s.

This model is a simple approximation of the real system, the parameters of the model is imprecise. In fact, accumulated through practice and experience of experts, we can see in this model: take a = 10. 3 J / m2, k = 0. 026 3 W / m2, = 119 s.

Model Predictive Control Toolbox in Matlab series provides model predictive control analysis, design and simulation functions. First, transform the transfer function model to the step response model which can be used for dynamic matrix control by function ploy2tfd ( ).Then set the controller's four weighting parameters and the scope of the constraints of the input and output. The weighting parameters are control step length P, predictive step length M, error weighed matrix q and control volume-weighted value R. Finally make a simulation by using the function cmpc ( ).

Use the control strategy and the model equations above, and simulate with Model Predictive Control Toolbox in Matlab simulation environment. The Greenhouse temperature is set at 21.5, the sampling time T is 20s, prediction horizon is set at P=10, and control horizon is set at M=5. The system response of DMC control is shown in Fig. 2, and the manipulated variables of DMC control are shown in Fig. 3. The system response of PID control is shown in Fig. 4, and the manipulated variables of PID control are shown in Fig. 5.

351

Fig. 2. The system response of DMC

Fig. 3. The manipulated variables of DMC

Fig. 4. The system response of PID control

Fig. 5. The manipulated variables of PID control

Comparing with the simulation results: 1) PID control has some shortages, such as slow response

speed, long time response (about 600s) and a little overshoot. It can also make the temperature decreased gradually. From Fig. 5 we can see that simple control measure causes the shortage of PID control. The PID control cannot be good to meet the requirements of control.

2) The dynamic matrix control overcomes the shortness. It has small overshoot, rapid response (about 160s), non-oscillation and good stability, but also has slight steady-state error. It can be seen from Fig. 3 that the manipulated variables change rapidly. Because of this, the dynamic matrix control can be good to meet the requirements of control.

Simulation results show that with the dynamic matrix control, the step response, response time, overshoot, and steady-state accuracy of greenhouse control system can meet the requirements. It indicates that the dynamic matrix control in the greenhouse control applications is feasible.

IV. CONCLUSION Traditional classical control theory can no longer meet the

requirements of the increasingly complex greenhouse control system. This paper attempts to utilize the dynamic matrix control theory in the greenhouse controlling system. It develops a control strategy of multi-step prediction, rolling optimization and feedback correction, based on the step response of the controlled object to improve the system robustness. The simulation results show that the plan is feasible, with a considerably long reaction time deficiency to be further improved. Above all, the simulation results show that the control algorithm is applicable in the greenhouse environment control. It can improve the existing greenhouse control algorithm in the field of agricultural engineering, and be consistent with the development of current greenhouse control technology. The paper proposes a preliminary exploration of the greenhouse predictive control method. And it may ask for further studies to apply the algorithm, or to realize the controlling system in practice.

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REFERENCES [1] J. Z. Wang, P. P. Li, and H. P. Mao, "Decision support system for

greenhouse environment management based on crop growth and control cost," Transactions Of The Chinese Society Of Agricultural Engineering, vol. 22, pp. 168-171, 2006.

[2] Z. Y. Wang, L. L. Qin, G. Wu, and X. T. Lu, "Modeling of greenhouse temperature-humid system and model predictive control based on switching system control," Transactions Of The Chinese Society Of Agricultural Engineering, vol. 24, pp. 188-192, 2008.

[3] F. W. Long, C. F. Zhang, and X. H. Bi, "Applications of DMC-PID algorithm in large time delay system," Electric Drive, vol. 38, pp. 50-52, 2008.

[4] M. Shen, R. B. Zhang, B. Q. Sheng, and Y. X. Song, "Predictive control method for greenhouse measurement and control system based on switch devices optimization combination," Transactions Of The Chinese Society For Agricultural Machinery, vol. 42, pp. 186-189,161, 2011.

[5] R. B. Zhang, F. H. Chu, X. L. Huang, and M. Shen, Predictive decoupled control of WSN nodes greenhouse environment simulation experimental system, Transactions of the Chinese Society for Agricultural Machinery, vol.43: pp. 192-196, 2012.

[6] J. Vasquez, J. L. Vasquez and C. M. Travieso, "Changing control rules dynamically in embedded digital control systems," WSEAS Transactions on Systems and Control, vol.5, pp. 143-152, 2010.

[7] C. Rodriguez, J. L. Guzman, F. Rodriguez, M. Berenguel, and M. R. Arahal, "Diurnal greenhouse temperature control with predictive control and online constrains mapping," in IFAC Conference on Control Methodologies and Technology for Energy Efficiency, CMTEE'2010, March 29, 2010 - March 31, 2010, Vilamoura, Portugal, 2010, pp. 140-145.

[8] A. Pawlowskia, J.L. Guzmna, J.E. Normey-Ricob, M. Berenguela, "A practical approach for generalized predictive control within an event-based framework," Computers and Chemical Engineering, vol.41, pp. 52-66, 2012.

[9] A. Ramirez-Arias, F. Rodriguez, J. L. Guzman, M. R. Arahal, M. Berenguel, and J. C. Lopez, "Improving efficiency of greenhouse heating systems using model predictive control," in 16th Triennial World Congress of International Federation of Automatic Control, IFAC 2005, July 3, 2005 - July 8, 2005, Prague, Czech republic, 2005, pp. 40-45.

[10] J. Lan, D. Li, N. Yang, and Y. Xi, "Implementation of dynamic matrix control on field programmable gate array," Journal of Shanghai Jiaotong University (Science), vol. 16, pp. 441-446, 2011.

[11] C. J. Huang, H. J. Liu, and D. F. Wang, "Simulation of boiler fuel combustion regulating system by using dynamic matrix control (DMC)," Process Automation Instrumentation, vol. 25, pp. 55-58, 2004.

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