Based on optimization procedures, control effort can be minimized which can be attained by the Least Effort (LE) control technique. Consequently, the control effort in this context is understood to be the maximum amplitude of the control signals or the integral of a specific control function.
A control strategy based on minimizing the control energy has been proposed two decades earlier. It concentrated on minimizing the control energy that needed to get a well- behaved system especially with disturbance rejection condition. It determines what is best possible in terms of optimal energy consumption through writing Performance Index as a mathematical expression. In general, the content of the Performance Index can alter according to the objective of the minimization process. It can be formulated with steady state errors, rise time, cost of operation and amount of required efforts. Consequently, many Performance Indices can be written for different control schemes and control objectives. The minimization procedure in this study incorporates specifying a Performance Index (sometimes called cost function) with content of control signals aiming to minimize the energy consumption. The control signals in this study are voltages on the inlet and exit fans, voltage on the chilled water pump and ambient
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heat transfer to ventilated volume which is temperature (equivalent to voltage) multiplied by inverse of thermal resistor (equivalent to electric resistor) according to Ohm law. The control inputs can be written in a form that includes the forward control gains, feedback control gains and system outputs (see section 4.5.3), where the control inputs are written as
1 1 2 1 1 1 1 2 2 2 2 2
1 2
( ) ( )
( )
m m
m m m m m
k h k h k h y t k h k h k h y t
k h k h k h y t
where ( ,k k1 2km)are the forward control gains, ( ,h h1 2hm) are the feedback control gains and ( ,y y1 2ym)are the system outputs. Detailed derivation is discussed in section 4.5.3 Squaring the control signals is a part of the calculation process that computes the energy spent by the control system. Applying the integration operation on the summation of the control inputs squared is indeed the optimization process execution. The optimization process will explore when the Performance Index Equation is minimum so that values of the forward and feedback gains at the minimum value of Performance Index Equation are corresponding to the minimum control energy to operate the HVAC plant and achieving in the same time well behaved system performance. It can be understood that the optimized control energy is the minimized energy to operate the plant so that without applying the optimization procedure the plant can dissipate higher control energy which is proportional to the cost of energy
The added value of optimizing the control efforts of a specific control technique can be recognised by comparing the control energy consumption by alternative control technique whose control energy is required to operate HVAC plant. It is highly recommended to research and to propose solutions of least control energy technique to contribute to the engineering efforts to achieve sustainable built environment.
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The control strategy based on minimizing the control energy has emerged from the British Control School and called Least Effort (LE) control technique. It was proposed for the first time by Whalley R. and Ebrahimi M. (1999) to control multivariable systems. The authors worked with their colleagues employing this technique on many further industrial processes.
They have obtained good results pertaining to decoupling the internal loops interaction of multivariable systems and improved the dynamics and the steady state responses with minimum control energy dissipation. Improved disturbance rejection was also achieved in their researches. Multivariable LE Control is a controller design method that uses the output feedback, proportional regulation and passive compensators so that the feedback structure is configured by inner and outer loops enabling improvements on transient, steady state and disturbance rejection associated with least control energy dissipation. The avoidance of employing active elements in the design procedure, such as integrators, is the major feature of this control methodology that enabled the researchers to accommodate many industrial applications, like automobile, military and aerospace systems. These industrial processes are characterized with limitations on the mass, inertia and space of power supply. The safe working span of the system components is also assured by the avoidance of integral controllers as its corrective actions is strictly increasing under sustained error conditions (Whalley R. and Ebrahimi M., 2006) . At the first stage, the design procedure aims to secure well-behaved system dynamics under the closed loop configuration. This design procedure is implemented through generating a specific polynomial function that forms the numerator of a transfer function whose denominator is the characteristic Equation of the system. This transfer function in turn is subjected thereafter to root locus design procedure to allocate the poles of the system at positions where the system has well behaved dynamics. Consequently, the coefficients of the generated polynomial will be selected to secure well behaved system dynamics and to be
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used in the Performance Index to find a solution for the gain ratios. Once the gain ratios values are computed and selected to make the Performance Index function minimum, they can be used simultaneously to compute the values of the forward gains and along with the generated polynomial. They can be used to compute the feedback gains as well. At the end, the forward and feedback gains are calculated with good secured system dynamics and minimized control efforts alike.
Thereafter, minimum coupling at the steady state system outputs responses can be achieved by pre-compensation, whereas the disturbance recovery can be enhanced satisfactorily by the outer feedback loop gains calibration associated with minimum control energy dissipation.
The LE control technique multivariable control has the same control concept of tradition multivariable control techniques, by employing decoupling compensators and close loop control elements to achieve accurate steady state values and to secure well behaved dynamics.
Figure 3.1 shows tradition multivariable control block diagram showing the close loop traditional PID control and decoupling compensators (Vhora, H. and Patel, J., 2016). LE control technique is using the same concept but with different control structure configuration.
The LE control technique utilizes an inner control loop employing forward and feedback control gains to secure the dynamics of the system responses and feedback outer loop to secure the accurate steady state responses as well as enhancing the disturbance rejection calibration.
Figure 4.10, in chapter four shows the block diagram of LE Controller showing the inner and outer loops configuration.
One more differentiator with the LE control technique is that it calculates the forward and the feedback control element gains based on the optimization process so the LE controller can attain a well-behaved system response but with least control effort dissipation.
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A LE control strategy has been proposed by Whalley R. and Ebrahimi M. (2004) to control a gas turbine system modelled as a two inputs two outputs multivariable system. A transfer function matrix was obtained and root locus on frequency responses methodology was followed in the design of an inner loop where the regulation of the system dynamics occurs.
An outer loop is used to secure steady state output accuracy with outer feedback loop for adjusting and enhancing the disturbance recovery with minimum control energy.
The control technique has been employed by Professor Whalley and his colleagues on many other applications. Whalley R. and Ebrahimi M. (2000) applied the control technique to regulate a mixing-tank liquid level. Whalley R. and Ebrahimi M. (2004) in another research study employed the same control technique on Automotive Gas Turbine application. The results in all the application have shown improved system dynamics, accurate steady state responses, minimum internal loops coupling and minimum control energy dissipation to recover the disturbances entering the system.
This project will employ the same concept by using the LE control technique on a HVAC system but modelled with more complexity by incorporation of HVAC system with three inputs
Figure 3.1. Block diagram of tradition multivariable control technique (Vhora, H. and Patel, J., 2016, pg2)
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and three outputs. The proposed solution herein aims also to obtain improved system dynamics, accurate steady state responses, minimum internal loops coupling and minimum control energy dissipation to recover the disturbances affecting the system. However, to show the claimed improvements, an alternative multivariable control strategy will also be employed, enabling a comparison study.
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