Modelling building energy systems - Control systems

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Lecture structure

  • Control systems - importance
  • PhD possibilities in this area

    • Summary

    In this lecture the student is introduced to the elements of control which may be applied in the built environment. The available control strategies are considered together with the implications for system modelling and simulation.

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    Course material (initial):

    6.6 Control system simulation

    In any plant system a number of control loops will exist, each one acting to control some region property (mass flowrate, fuel supply rate, etc.) on the basis of detected signals which define some deviation from the controlled variable set point. Traditionally the approach to this problem is to establish a simplified model of the process - a simple first order lag model with gain and dead time is not uncommon - and then to combine this with a controller model to give some overall transfer function for the system (by the Laplace transform technique of chapter 2 for example).

    Underlying this section is the assumption that the process model is already established in matrix form as described in previous sections. The objective then is to solve this matrix system in terms of control system characteristics or, alternatively, to incorporate a model of the control loop(s) within the matrix equation. For the present purpose, a control loop is considered to be comprised of:

    The basic operational principles underlying these elements, and their application to control the operation of building plant, is described in a number of texts [Letherman 1981, Wolsey 1975] and current research activity is concerned to develop adaptive control systems which rely on an in-built model (usually contained on a single micro chip) of the process they control [Dexter 1983 & 1984]. For this reason no attempt is made here to define control terminology [see BS 1967] or to discuss the philosophy of control application. Instead this section describes how, if the relevant control details are available, control theory is used to dictate the solution of the combined building/plant matrix system previously derived in this chapter and chapters 3 and 4.

    There are two techniques which can be used for this purpose:

    1. At each time-step as a simulation proceeds, the nodal property detected by the sensor is fed to some independent algorithm representing controller response. Note that this property must be one of the variables held in the matrix equation future time-row state vector.

      The controller algorithm then acts to fix or limit some other nodal property, via the actuator node, prior to matrix reformulation for the current time-step. In this way simulation control can be achieved on the basis of a prevailing control point deviation (proportional control), control point deviation rate of change (derivative control) or the control point deviation past history (integral control) of any individual or multiple node test - that is the sensor could be a room stat sensing air temperature or, perhaps, sensing some weighting of air and surface temperatures. Controller types can be combined (P+I etc) and the effects of dead times and sensor/actuator response rates (if known) included by incorporating a softwarememory facility so that any control action can be delayed until some later matrix inversion with current action arising from previous sensor detection.

      For a proportional controller, the control algorithm will take the form:

      Eq. 6.36

      where,

      = deviation of the input signal from the set point

      = change in output signal

      Kp = proportional gain factor

      The proportional gain is ideally a constant and is dependent on the adjustment of the controller. To improve controller response or to remove offset, derivative and/or integral control is often added to the basic proportional control action. Derivative action is defined by:

      where, Td is the derivative action time; and for integral action:

      where, Ti is the integral action time. Any mixed scheme can now be established:

      and the controller algorithm follows from a knowledge of the controller gain and derivative and integral action times. Note however that this information may be subject to extreme uncertainty and is often difficult to obtain from the manufacturers of control equipment.

    2. An alternative procedure is to locate an equation set - representing sensor, controller and actuator operation - within the building/plant matrix equation. Consider a thermostatic radiator valve as required by the wet central heating system of section 6.4. Here the sensor is a wax filled capsule which can expand against a spring to cause the valve to throttle water flow. The valve stroke is therefore a continuous function of the sensed temperature deviation and so control action is effectively proportional. Valve manufacturers will normally have data available which describes the relationship between sensed temperature and valve position and between valve position and flow rate. This data can then be re-expressed in the form of figure 6.11 so that, accepting linearity for the present purpose, the proportional gain can be determined against any operating pressure.

      Figure 6.11 Characteristic curves for a thermostatic radiator valve.

      Applying a simple energy balance to the wax capsule gives the following first order ordinary differential equation:

      where,

      is the wax density

      C = wax specific heat

      V = capsule volume

      hi= heat transfer coefficient associated with heat exchange i

      = sensor temperature

      = surroundings temperature (air or surface)

      q = additional heat gain (from water flow for example)

      Replacing the derivative by a finite difference approximation, and by the usual process of present and future time-row equation concatenation, gives the final sensor simulation equation emerges as:

      Eq. 6.37

      This equation defines sensor response and can be incorporated within the matrix equation giving, at each time-step, the sensor temperature to allow mass flowrate assessment (from equation 6.36) for the following time-step. Note that equation (6.36) cannot be included in the matrix equation since the control variable, mass flowrate, is not held in the matrix state vector but is an element of the coefficient entries.

      Any number of control loops can be imposed on the simulation allowing control system evaluation and realistic energy consumption estimates.