- 19 - VENTILATION CONTROL OF THE BLANKA TUNNEL: A MATHEMATICAL PROGRAMMING APPROACH Pořízek J. 1, Zápařka J. 1, Ferkl L. 1 Satra, Czech Republic Feramat Cybernetics, Czech Republic ABSTRACT The Blanka tunnel is a 5.7 km long highway tunnel under construction in Prague, Czech Republic. Because of its complicated topology and very strict environmental restrictions, the synthesis of ventilation control for normal conditions turns out to be fairly challenging. The air flow is restricted to leave the tunnel through traffic portals it has to be aspirated by ventilation centers and released by exhaust shafts and chimneys. To achieve this goal, control strategy was designed based on the mathematical programming principles. The designed controller, which is inspired by model-based predictive controllers (MPC) used in heavy industry, is energy optimal by definition, adapts to changes in operational conditions and requires significantly less design time than traditional approaches. Keywords: ventilation control, city tunnels, model-based predictive control 1. INTRODUCTION After its opening scheduled for 11, the Blanka tunnel (see Figure 1) will form a part of the inner ring of Prague. Because of its complicated topology, strict operational demands and axial ventilation system, the ventilation control does not have a straightforward solution. After several attempts to use conditional control ( if-then-else type), we decided to turn to modern control algorithms and to use model-based predictive control (MPC) to achieve the control objectives. Figure 1: The Blanka tunnel in Prague th International Conference Tunnel Safety and Ventilation 8, Graz
- 193 -. MPC CONTROL PRINCIPLES The MPC control is an optimization strategy that minimizes an optimality criterion (cost function) over a finite time horizon. Its first use was in 197 s in oil industry and is widely used for optimal control of slow industrial processes today. The main advantages of the MPC control are: It handles multivariable control very naturally It can take actuator limitations into account It allows to define control constraints It is very intuitive to tune For tunnels, the structure of the MPC controller is illustrated on Figure. Figure : MPC controller block diagram For the case of tunnel ventilation control, we use a linear model (which will be discussed further), the cost function has a quadratic form (1) wherein x denotes system states and u denotes system control signal. It is obvious that by means of matrices Q and R, we may directly influence the cost of system states and control signal. The linear constraints have a form () so we can impose physical constraints that exist in the system. We have to point out that the MPC controller is not a classical, linear controller in the usual sense. It is rather an optimization procedure that optimizes the trajectory of the output signal, while trying to minimize the energy consumption of the system (through the cost function) and maintaining the physical or technological limitations of the system (through constraints). 3. TUNNEL CONTROL MODEL The basic assumption for the control model is that the air flow has two major contributors the air flow generated by ventilation system Q f and the remaining air flow Q* (3) th International Conference Tunnel Safety and Ventilation 8, Graz
- 19 - Moreover, according to measurements from the Mrázovka tunnel (Pořízek, 7), the air flow can be further expanded to () wherein f i is the power input to the ventilation equipment in the i-th section of the tunnel and a is a suitable linearization coefficient, obtained by simulation or measurement. The derivation of the simulation model was already presented in (Ferkl, 7), with the resulting formula for the pollution level in a tunnel section being (5) wherein k is the exhaust production coefficient for a single vehicle, n is the number of vehicles and s is the length of the i-th tunnel section. Referring to our previous results (Ferkl, 7), the optimization process (which turns out to be an MPC controller) that aims to achieve the exhaust inside the tunnel to lie within given limits and the air flow to have the desired direction, is (6) The cost function weights the power input to respective ventilation fans (first line) and minimizes the switching of the fans (second line) for enhancing the lifetime of the ventilation equipment. It minimizes the sum of cost functions for all tunnel sections ( norm) according to a quadratic criterion ( norm). Equation (6) is a representation of a mathematical program. The constraints limit the power input f to the ventilation equipment (first line), imposes the exhaust limits through minimum required air flow Q (second line) and, if needed, requires a negative air flow for tunnel section in a set K (third line).. SIMULATIONS To make the presentation of our results more comprehensive, we will only present the control for the northern tube of the Blanka tunnel only; however, the southern tube is similar to the northern one. Figure 3: Control sections of the Blanka tunnel, as referred to in the text. The geometry of the northern tube is shown in Figure 3. The tunnel is divided into control sections 1 to 1. Sections no. 13 and 1 represent a ventilation center. The figure also shows the preferred air flow directions for a closed mode of operation, wherein the only passage for the air to leave the tunnel is the ventilation center (i.e. section 13). th International Conference Tunnel Safety and Ventilation 8, Graz
- 195-1 3 5 6 7 8 9 1 11 1 13 1 - - - - - - - - - - - - - - -..1..67.9 1.13 1.36 1.59 1.8.5 Figure : Simulation of MPC control for the Blanka tunnel. could get a signal that is more fancy than the original two separate signals. In the following simulations, we use normalized power output equivalent to nominal power of an average jet fan installed inside the tunnel. Instead of using time characteristics, we show the results on static characteristics, wherein the power input to the ventilation equipment is the dependent variable and the value of the residual air flow (Q* in Equation (3), which represents the measured air flow minus the air flow contributed by the ventilation system). Figure shows the result for the MPC controller without any preferences for the cost function (all power inputs are weighted equally). Unlike for linear controllers (such as PID controllers), the plots are not smooth. This is the result of the constraints the controller distributes the power according to the capacities of the respective fans, in order to maintain the overall energy consumption minimal. This is something that is very difficult to achieve by purely linear controllers. Numerical difficulties may appear in some cases, as the air flow model is poorly conditioned in principle and the controller sometimes hesitates, which ventilator to use. It may be seen from the figure that by combining sections 1 and together, we Figure 5 shows a comparison of three simulations with different cost functions. The performance of the controller is illustrated by the end-section of the tunnel (sections 7, 8, 1, 1), which is interesting for comparison because the tunnel operates in a closed mode, the air flow in section 8 has to be reversed. In said simulations, the following conditions were set through the cost function: 1. Ventilation in all sections has the same cost.. Sections 9-1 (onramps) are penalized, i.e. their use has to be minimized. 3. Sections 9-1 are penalized, while the use of section 1 (the ventilation shaft) is preferred. th International Conference Tunnel Safety and Ventilation 8, Graz
- 196 - Simulation No. 1 Simulation No. Simulation No. 3 Section 7 - -..39.81 1. 1.6.5 - -..39.81 1. 1.6.5 - -..39.81 1. 1.6.5 Section 8 - -..39.81 1. 1.6.5 - -..39.81 1. 1.6.5 - -..39.81 1. 1.6.5 Section 1 - -..39.81 1. 1.6.5 - -..39.81 1. 1.6.5 - -..39.81 1. 1.6.5 Section 1 - -..39.81 1. 1.6.5 - -..39.81 1. 1.6.5 - -..39.81 1. 1.6.5 Figure 5: Comparison of controller tuned according to various cost functions. The results show again a non-smooth behaviour, as the controller tries to balance the energy consumption. The first simulation is not quite desirable, as we can see that the controller counteracts by sections 1 and 1. Indeed, this is the controller with a uniform cost function. The second simulation is much better; we can see the effect of penalizing the onramp (section 1). The third simulation gives the best results, it even has quite smooth signal. The reason may be that preferring the ventilation shaft against other ventilators is natural, so it suits the controller the best. 5. CONCLUSIONS We have shown an approach to ventilation control, which is based on MPC controller. This type of controller is widely used in industry, especially for large scale systems with multiple inputs and multiple outputs. This makes it an ideal tool for tunnel ventilation control, especially for city tunnels, where special requirements have to be met. 6. REFERENCES Ferkl L., Meinsma G. (7) Finding Optimal Control for Highway Tunnels. Tunnelling and Underground Space Technology, vol., issue, pp. -9. ISSN 886-7798. Pořízek J., Ferkl L., Sládek O. (7) Road Tunnel Ventilation Model: Simulation Analysis. Tunnel Management International, vol. 9, no. 1, pp. 65-7. ISSN 163-X. th International Conference Tunnel Safety and Ventilation 8, Graz