Design Of Discrete Time Model Predcitive Controller Engineering Essay

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Abstract- This project paper proposes the Designing of Discrete Time Model predictive controller (DMPC) for Drum Boiler-turbine used in thermal power plant. Drum boiler model is chosen here for analysis is famous ASTROM Model. it is considered MIMO system with Three input and three output. Nonlinear model of boiler is linearised to Operating point and Model predictive controller is designed. Then, the control performances of Model Predictive controller are simulated with control input constraints and difference constraint .finally results thus evaluated Performance for Linearised plant. But This is not sufficiently suitable for Non linear plant as the operating Point are not generally same in real plant.

Keywords : Model predictive controller(MPC),Drum boiler, shrink / swell, non minimum behavior,MIMO



Drum Boiler-turbine system supplies high pressure steam to rotate the turbine in thermal electric power generation. The purpose of the boiler-turbine system control is to meet the load demand of electric power while maintaining the pressure and water level in the drum within tolerance. This boiler-turbine system is usually modeled with a Multi-Input Multi-Output (MIMO) nonlinear system .The severe nonlinearity and wide operation range of the boiler-turbine plant have resulted in many challenges of power system control engineers.

The following are sub control systems of the thermal power plant Boiler Steam Generation control, Turbine Speed control ,Coal Feeding Control ,Feed water Control ,Fuel flow control ,Air flow control, Cooling water Control, Auxiliary equipment control Switch yard control, Ash Disposal control, Compressed Air control for Valves. Reverse Osmosis water plant control, Demineralised water control, Hydrogen gas Generation Control

In power plants Drum boiler with water wall model with Multi fuel firing is used. Water Forced circulation or natural circulation type used. It consists of a cylindrical drum in which two headers are connected. Down comer header receives water from drum ,then water reaches water wall where upon firing is being done. therefore steam/water mixture in wall moves up through Riser header finally reaches back drum. from drum steam is separated using cyclone system then goes to turbine through various further stage of steam heating by flue gas such Super heaters, Reheaters (reheating the steam coming from exhaust first stage High pressure Turbine flows to Intermediate turbine).

Fig. 1. Drum Boiler Schematic Diagram


In the drum-type boiler-turbine system, drum water-level control is considered to be a more difficult problem, main reason being a non-minimum phase behavior due to shrink / swell and instability because of the integrating properties of drum-level dynamics .Although many successful applications of conventional controllers to various industrial plants have been reported, it is difficult to find the application of MPC to drum-type boiler-turbine system. But now a days the trend changing. Companies like ABB successfully implemented Model predictive controller some plants.

Practical design of a MPC, one of the most important steps is the development of a model to describe the system dynamics. Here the augmented model of plant are considered for the model for development DMPC. One when the exact nonlinear mathematical model is given, the model can be found by linearizing the nonlinear model, and. A DMPC is designed for model, and the control performances are evaluated. The prime objective this research work is to Design Discrete Time Model Predictive controller for Drum boiler are Costly outage of power plant can be averted ,Life of Drum and water walls can be increased as less impact of severe fluctuating thermal stress. Eliminating high skilled operator requirement to control boiler and Stable operation of plant over wide varying demand.


ẋ1 = -0.0018u2x19/8 + 0.9u1 - 0.15u3 (1)

ẋ2 = [(0.73u2 - 0.16)x19/8 - x2]

10 (2)

ẋ3 = [141u3 - (1.1u2 - 0.19) x1]

85 (3)

y1 = x1 (4)

y2 = x2 (5)

y3 = 0.05(0.13073x3 + 100acs + qe - 67.975) (6)



αcs = (1 -0.001538x3) (0.8x1 - 25.6) (7)

x3(1.0394 - 0.0012304x1)

qe = (0.854u2 - 0.147)x1+45.59u1-2.514u3-2.096 (8)

The three inputs are u1 is fuel flow, u2 is steam flow to the turbine,u3 is feed water flow to the drum .All are normalized positions of valve actuators, Three state variables are x1 is drum steam pressure, (P in kg/cm2 ), x2 is electric power

(E in megawatt) and x3 is steam water fluid density in the drum (ρf in kg/m2 ).The three outputs are y1 is drum steam pressure,y2 is electric power in Mega watt and y3 is drum water level in metre.

Position of valve actuators are constraints

-0.007≤ du1≤ 0.007 (9)


-2.0 ≤ du2 ≤ 0.02 dt (10)

-0.0≤5 du3≤ 0.05 (11)


Linearizing using Taylor series at an Operating Point y0=(115,85,0);X0= (115,85,402.759); u0=(.0414,0.778,0.543) therefore state space model is obtained as follows.





Y(s)=[C(sI-A)-1 B+D]U(s) = U(s) (16)










Equation 1 to 8 Refers linearised model of Astrom boiler. equation 12 to 16 and state space model linearised state space matrices of model. using equation nine numbers transfer functions obtained (equation 17 to 25).The step response of boiler turbine scheme is shown in figure .2. Drum pressure and power flow settles .but the drum level keeps on increasing .therefore it needs control.

Figure.2 Unit Step Response Of Boiler Turbine



The original plant model is augmented with integrators and the DMPC design is performed on the basis of the augmented state-space model, it is important for control system design that the augmented model does not become uncontrollable or unobservable, particularly with respect to the unstable dynamics of the system. Controllability is a pre-requisite for the predictive control system to achieve the desired closed-loop control performance and observability is a pre-requisite for a successful design of an observer. Because the augmented model introduced additional integral modes, we need to examine under what conditions these additional modes become controllable .The simplest way for the investigation is based on the assumption of minimal realization of the plant model.thus augmented model is obtained which is used for prediction. the future is predicted in of terms of current state information using optimizing we find the incremental value of control signal subject the valve movement position rate change and amplitude control.this is suitablely formulated hildreth quadratic programming procedure.the first movement of optimized control trajectory is imposed over plant and the procedure is repeated for further subsequent step. we use 'soft' instrument used to estimate unknown state variables based on process measurement, in a control engineering context, is called an observer. The Proposed scheme Discrete MPC to boiler control system is shown in figure


The Discrete Time Model predictive controller designed simulated Astrom Boiler model three input and three output MIMO system and response graph obtained shown in figure 4. DMPC controller works well output giving satisfactory with specified constraints. the constraint DMPC is more suitable to Real time implementation .Rate change constraints also satisfied. Power flow, drum level, drum pressure stabled to set value .in open loop pressure , power flow takes nearly 180 sec to settle. Similarly pressure also settles at 180 sec and Drum level keeps slightly increasing and comes to stable within variation ±0.4 m. This value is acceptable for practical reason. For the value of 0.6 DMPC tuning parameter 'a' Time scaling factor ,all process variable settles as given table.1 for set point process references 3 level. DMPC gives good set point tracking. Here it is found that the variation in drum level keeps on decreasing subsequent steps from initial step (±0.1 m).

Figure 4 .DMPC Controller Outputs and Process Outputs

Table.1 Performance analysis for DMPC Tuning parameter a=.6

Process Output

Set point 3 level

Settling time (Sec)

Over shoot

Drum pressure








Drum level



±0.4 m


This Project paper presents the application of Discrete Time Model Predictive controller to a drum-type boiler-turbine system. Astrom Nonlinear Model linearised to operating point investigated. The DMPC controller output constraints are investigated in design. Because of the high nonlinearity of the drum water-level dynamics, the linearised model is not accurate for relatively large changes in step inputs. Thus it is concluded that some other technique needed to be used for better responses. ConsequentlyDMPC designed with the Astrom model shows better results with controller output constraints. It also shows good tracking performance and has benefit when considering the input/output constraints, which is often the case in real industrial systems. The novel contribution of this project paper is as follows:

First, it has been shown that the wide-range nominal operation of drum-type boiler-turbine system can be effectively controlled by a direct application of Discrete MPC. Until now, the direct application of conventional controller to drum-type boiler-turbine system was found to be difficult due to the drum-level dynamics with instability and the non minimum phase. So Discrete Time MPC gives better performance .Second, the linearised model of drum-type boiler-turbine system is shown not to be valid for a long-range prediction of Discrete MPC, main reason being the poor quality of linearised drum water-level dynamics. Therefore, a careful validation of the model is necessary in designing the DMPC, although a valid mathematical model is used in this research.

Future Work

Since model here is selected linearised to operating point , gives poor response to different operating point. the inclusion of adaptive fuzzy model where many operating points may be considered. depending on any operating condition the model dynamically modified using fuzzy logic.