3.3.1.3 Proportional Integral Derivative Controller (PID) The Proportional Integral Derivative controller has a derivative part that increases damping in the system. The stable limit cycles are achievable due to the presence of integral. The small gains are applied to the system so that the system would be stable. However, the response is slow. The transfer function of the Proportional Integral Derivative controller is shown as:
D(s)=K_p+K_d s+K_i/s (3.37)
3.3.2 Control Strategy of PID Controller In order to control the system, every gain in PID controller needs to be tuned to get desired response. There are several tuning methods used for PID controller which are Manual Tuning, Ziegler-Nichols, Software tools and Cohen-coon. However,
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The controller design based on MIT rule can be produced with any system by using MRAC scheme including electro- pneumatic position system. The equations for this rule are described as follows (Jain and Nigam, 2013): The cost function of this rule is expressed as:
J(θ)=e^2⁄2 (3.38) where θ is adjustable parameter and e is the error between plant output and model. To minimize the cost function to zero, parameter θ is adjusted where the change in parameter is put in negative gradient in direction of J :
dθ/dt=-γ ∂J/∂θ
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For equation (35), the cost function J(θ) will be reduced to zero because of the changes of parameter θ with respect to times. The combination of Eq. (3.38) with (3.39) produces
dθ/dt=-γe ∂e/∂θ (3.40)
where the sensitivity derivative ∂e/∂θ indicates the change of error which relates to the parameter θ.
3.3.4 Control Strategy of MIT Rule Model Reference Adaptive Control (MRAC) is a strategy used in designing an adaptive controller that relates to the controller parameters adjustment in order for the actual plant output follows the reference model output that consists of same input reference. There are three components used in designing MRAC method besides the system plant itself. The components are (Jain and Nigam, 2013):
Adjustment Mechanism: a component used to alter the controller parameters for the tracking of the actual plant to the reference model by using mathematical approaches such as Lyapunov theory and MIT rule. Controller: a set of adjustable parameters Reference Model: provides idyllic response to reference input from adaptive control
A maglev system is nonlinear and its open-loop response is unstable because of the nature of the magnetic forces used. PI controllers are based on a linearized model, so they do not compensate for certain variations. These variations can occur when a magnetic bearing experiences a working load change on the rotor during operation, ...
i.e. K ̇(t)=sY(t)-δK(t), L ̇(t)=nL(t) and A ̇(t)=gA(t) it is important to consider the new assumptions that concern the newly added inputs.
Rockis, Gary, and Glen Mazur. Electrical Motor Controls for Integrated Systems. 4th ed. Homewood, IL: American Technical, 2009. Print
F = x/y = lFl x ((δx/IxI) + (δy/lyl)) was used for the error propagation of 1/d where x = 1 and y = d. This equation was also used for the error propagation of κ = slope/ ε0A where x = slope and y = A.
It is a step of defining the goals of the projects and the results are aimed at reaching certain levels of productivity of customer satisfaction. The second stage is measure, and it is the stage of collecting data and facts and evaluating current operational performance. The third stage is analyze with the purpose of developing methods and theories that will best suit the solving of the problem; it is also a stage of detecting cause-and-effect ties of the processes. The fourth stage is improve, it is aimed at generating ideas for reaching the desired process improvement. Finally, there is the control stage that is about monitoring the operations to find out whether the process of improvement is smooth and the problems were solved (Meredith & Shafer,
In this approach, the focus will be on the internal control objectives so that the control design can be well assessed. First, the auditor will define the control measures and objectives and then find out which measures already installed meet the objectives (Tyrer, 1994).
Barbara Mowat and Paul Warstine. New York: Washington Press, 1992. Slethaug, Gordon. A. See "Lecture Notes" for ENGL1007.
The report highlight’s the essential aspects of the control process. In terms of concurrent feedback as well as feed forward, that companies can use to implement so that they can have better outcomes in terms of efficiency of the business. Consequently the report underlines as well as emphasizes of the many contributing factors of these controls. The authors have contrasting views on the control models of an organization, they believe that in order to create an effective control process, and organization first needs to determine its strategic plans for instance in terms of what it is and where is it going.
Lastly, the controls stage is defined as the stage where a company designs its marketing plan it must note that there is not a fixed position with no variability, therefore the marketing plan must be updated due to emerging external factors that might affect the strategy as a whole, as long as it moves towards fulfilling the requirement of the consumer using this telecom organization.
The integro-differential equations are originated from different mathematical models for many scientific phenomena. Nonlinear integro-differential equations are also can be seen in various applications of various scientific fields that are modeled by nonlinear phenomena.[3]
Controlling is the fourth management function and its purpose is straightforward- to make sure that actual performance meets or surpasses objectives. It is well used for decision making and problem solving. Effective control depends on other management functions and it gives feedback to them. These functions are planning, organizing and leading. Planning sets directions and allocates resources. Organizing puts people and material resources together in working combinations. Leading motivates people to use these resources in the best way. Basically, the function of controlling is to make sure that the right things happen in a right time and in the right way.Control helps that overall directions of individuals and groups are consistent with short-range and long-range organizational plans. Also, it helps to ensure that objectives and accomplishments are coherent with one another throughout an organization. Moreover, it helps maintaining fulfillment with essential organizational rules and policies. Good example where we can see role of control is in helping to protect individual rights to become equivalent with employment opportunities at work. The control process practiced by managers includes four steps: 1) establish objectives and standards 2) measure actual performance 3) compare results with objectives and standards and 4) take actions if necessary1. The controlling process starts with establishing performance objectives and standards which means that the controlling process begins with planning. Performance objectives should be defined and associated with specific measurement standards for determining how well they are accomplished. Standards are the targets of performance. The next step of the control process would be measur...
In process industries control refers to the regulation of all aspects of the process. Precise control of temperature, pressure, level and flow is important in many process applications.
The purpose of this report is showing how to apply the control process in the
whereβ the intercept 0 and β the slope 1 are unknown constants and ε is a random error component .
Differential calculus is a subfield of Calculus that focuses on derivates, which are used to describe rates of change that are not constants. The term ‘differential’ comes from the process known as differentiation, which is the process of finding the derivative of a curve. Differential calculus is a major topic covered in calculus. According to Interactive Mathematics, “We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).” Not only are derivatives used to determine how to maximize or minimize functions, but they are also used in determining how two related variables are changing over time in relation to each other. Eight different differential rules were established in order to assist with finding the derivative of a function. Those rules include chain rule, the differentiation of the sum and difference of equations, the constant rule, the product rule, the quotient rule, and more. In addition to these differential rules, optimization is an application of differential calculus used today to effectively help with efficiency. Also, partial differentiation and implicit differentiation are subgroups of differential calculus that allow derivatives to be taken to more challenging and difficult formulas. The mean value theorem is applied in differential calculus. This rule basically states that there is at least one tangent line that produces the same slope as the slope made by the endpoints found on a closed interval. Differential calculus began to develop due to Sir Isaac Newton’s biggest problem: navigation at sea. Shipwrecks were frequent all due to the captain being unaware of how the Earth, planets, and stars mov...