It is desirable to use well-designed controllers to maintain building temperature with solar collector space-heating systems....

  

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It is desirable to use well-designed controllers to maintain building temperature with solar collector space-heating systems. One solar heating system can be described by [10] dx 3x1 + u + uz, dt and dx2 = 2x2 + uz + d, dt where x1 = temperature deviation from desired equilibrium, and x2 = temperature of the storage material (such as a water tank). Also, ul and u2 are the respective flow rales of conventional and solar heat, where the transport medium is forced air. A solar disturbance on the storage temperature (such as overcast skies) is represented by d. Write the matrix equations and solve for the system response when ul = 0, u2 = 1, and d = 1, with zero initial conditions. It is desirable to use well-designed controllers to maintain building temperature with solar collector space-heating systems. One solar heating system can be described by [10] dx 3x1 + u + uz, dt and dx2 = 2x2 + uz + d, dt where x1 = temperature deviation from desired equilibrium, and x2 = temperature of the storage material (such as a water tank). Also, ul and u2 are the respective flow rales of conventional and solar heat, where the transport medium is forced air. A solar disturbance on the storage temperature (such as overcast skies) is represented by d. Write the matrix equations and solve for the system response when ul = 0, u2 = 1, and d = 1, with zero initial conditions.