# Optimal performance index and control formulas

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The payback period formula is used to determine the length of time it will take to recoup the initial amount invested on a project or investment. The payback period formula is used for quick calculations and is generally not considered an end-all for evaluating whether to invest in a particular situation. The notion of a performance index is very important in estimator design using linear-state-variable feedback, which is presented in Sections 8.1 through 8.6, and in optimal control theory, where the system is designed to optimize this performance index given certain constraints. This subject will be discussed fully in Chapter 11. The most widely used measure of practical control performance is the decay ratio as it gives a good indication of the stability of the controlled response. An often used rule for controller tuning is 'one-quarter decay ratio', where the controller is tuned to produce a decay ratio of 1/4 (the second peak is a quarter the height of the first).

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The formula to calculate Cmk is same as Cpk, but the standard deviation used here is sample standard deviation. But, for Cpk standard deviation is measured from the control chart, as this is a measure of process performance. Cmk is measured using continuous samples keeping all influences other than the machine parameters constant. Optimal control based on a modified quadratic performance index for systems disturbed by sinusoidal signals. Organization’s size and span of control. Organization’s size is determined by number of its employees, the largeness of its operation, and its market reach and share. It also poses a very different challenge for the organization’s leaders, while small organizations are build for innovation, large are meant for operational efficiency.

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The key performance indicators (excepting waste) are expressed as a ratio of the total annual environmental impact (carbon emissions, electricity consumption, gas, oil and heat consumption, paper and water consumption) divided by the number of equivalent employees. 1.1.1 Energy and water In process improvement efforts, the process performance index is an estimate of the process capability of a process during its initial set-up, before it has been brought into a state of statistical control. • Control Problem: change temperature of unit to x d within time t f; "consume minimum amount of fuel. Allow for a tolerance δ. • Performance Index J(u) of control system: measure of total cost of control and accuracy generated in time period [0, t f] by control u. Generally: • Optimal control u*(t) with performance index J*.

Module 6 – Metrics, Performance Measures and Forecasting 18 Prepared by: Booz Allen Hamilton Performance Indices The Cost Performance Index (CPI)is a measure of Cost Efficiency. The CPI measures the value of work performed against the actual cost. Cost Performance Index (CPI) = EV/AC If the result is less than 1.0, cost is GREATER than budgeted Performance. Performance takes into account anything that causes the manufacturing process to run at less than the maximum possible speed when it is running (including both Slow Cycles and Small Stops). Performance is the ratio of Net Run Time to Run Time. It is calculated as: Performance = (Ideal Cycle Time × Total Count) / Run Time

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In process improvement efforts, the process performance index is an estimate of the process capability of a process during its initial set-up, before it has been brought into a state of statistical control. Optimal control • Performance index and constraints • Programmed control – compute optimal control as a time function for particular initial (and final) conditions • Optimal control synthesis – find optimal control for any initial conditions – at any point in time apply control that is optimal now, based on the current state. This ... Mar 11, 2014 · Demonstrates how predictions based around the global unconstrained optimal can be substituted into the performance index to give a simple cost function. Introduces the augmented model as a ...