The headbox process is used in the manufacture of paper to transform the pulp slurry

Chapter 0, Problem DP11.5

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The headbox process is used in the manufacture of paper to transform the pulp slurry flow into a jet of 2 cm and then spread it onto a mesh belt [22]. To achieve desirable paper quality, the pulp slurry must be distributed as evenly as possible on the belt, and the relationship between the velocity of the jet and that of the belt, called the jet/belt ratio, must be maintained. One of the main control variables is the pressure in the headbox, which in turn controls the velocity of the slurry at the jet. The total pressure in the headbox is the sum of the liquid-level pressure and the air pressure that is pumped into the headbox. Because the pressurized headbox is a highly dynamic and coupled system, manual control would be difficult to maintain and could result in degradation in the sheet properties. The state-space model of a typical headbox, linearized about a particular stationary point, is given by -0.8 -0.02 + 0.02 0 x + 0.05 0.001 FIGURE DP11.4 Helicopter pitch angle, 0, control. and y [1 0]x. The state variables are x\ - liquid level and .r2 = pressure. The control variable is ux = pump current. (a) Design a state variable feedback system that has a characteristic equation with real roots with a magnitude greater than five, (b) Design an observer with observer poles located at least ten times farther in the left half-plane than the state variable feedback system. (c) Connect the observer and full-state feedback system and sketch the block diagram of the integrated system.