![Results:
Second Order Transfer Function Model:
The second order instance generates a transfer function with the following equation:
where K is the steady-state value of the response in the case of a unit step input, wn is the natural
frequency, and is the damping ratio.
PID Model:
Proportional Gain (Kc) represents the proportional gain of the controller. In the equation that defines
the PID Academic form, Kc represents the proportional gain. The default is 1. Integral Time [s] (Ti)
is the controller parameter that adjusts the effect of the error integral term E(s)/s on the controller
output U(s). In the equation that defines the PID Academic form, Ti represents the integral time. The
default is 0. Derivative Time [s] (Td) is the controller parameter that adjusts the effect of the error
derivative term sE(s) on the controller output U(s). In the equation that defines the PID Academic
form, Td represents the derivative time. The default is 0. The default PID Academic controller does
not use derivative time. error in describes error conditions that occur before this node runs. This
input provides standard error in functionality. High Frequency Time Constant [s] (Tf) is the low pass
filter time constant Tf this VI uses to make the PID model a proper system. The default is 0. Transfer
Function Model returns the transfer function this VI constructs based on the inputs. To access and
modify the data in the model, use the Model Information VIs. error out contains error information.
This output provides standard error out functionality.
Series State-Space:
Two linear models are connected in series. The system models either must be continuous-time
models or must have the same sampling time if they are discrete-time models. Wire data to the
Model 1 and Model 2 inputs to determine the polymorphic instance to use or manually select the
instance.
Feedback Model:
Connects two linear models in feedback configuration. The system models either must be
continuous-time models or must have the same sampling time if they are discrete-time models. Wire](https://image.slidesharecdn.com/exp7robotics-170309114736/85/Design-the-implementation-of-CDEx-PID-with-Constraints-4-320.jpg)
Design the implementation of CDEx PID with Constraints
- 1. EXPERIMENT 7 AIM: To study and design the implementation of CDEx PID with Constraints. Apparatus Used: Microsoft Windows XP Professional Version 2002, Intel(R) Pentium(R) Dual CPU, E2180 @2.00 GHz, 2.00 GHz, 1.99 GB of RAM, LabVIEW Robotics 2011 SPI. Theory: LabVIEW (short for Laboratory Virtual Instrumentation Engineering Workbench) is a platform and development environment for a visual programming language from National Instruments. Short for Laboratory Virtual Instrument Engineering Work bench is a programming environment in which you create programs using a graphical notation (connecting functional nodes via wires through which data flows); in this regard, it differs from traditional programming languages like C, C++, or Java, in which you program with text. However, LabVIEW is much more than a programming language. It is an interactive program development and execution system designed for people, like scientists and engineers, who need to program as part of their jobs. The LabVIEW development environment works on computers running Windows, Mac OS X, or Linux. LabVIEW can create programs that run on those platforms, as well as Microsoft Pocket PC, Microsoft Windows CE, Palm OS, and a variety of embedded platforms, including Field Programmable Gate Arrays (FPGAs), Digital Signal Processors (DSPs), and microprocessors. Procedure: Execution is determined by the structure of a graphical block diagram on which the programmer connects different function nodes by drawing wires. These wires propagate variables and any node can execute as soon as all its input data become available. LabVIEW ties the creation of user interfaces (called front panels) into the development cycle. LabVIEW programs/subroutines are called virtual instruments (VIs). Each VI has three components: a block diagram, a front panel, and a connector panel. The last is used to represent the VI in the block diagrams of other, calling VI. Controls and indicators on the front panel allow an operator to input data into or extract data from a running virtual instrument. However, the front panel can also serve as a programmatic interface. Thus a virtual instrument can either be run as a program, with the front panel serving as a user interface, or when dropped as a node onto the block diagram, the front panel defines the inputs and outputs for the given node through the connector pane. This implies each VI can be easily tested before being embedded as a subroutine into a larger program. The graphical approach also allows non-programmers to build programs simply by dragging and dropping virtual representations of lab equipment with which they are already familiar.
- 2. Execution of VI’s and Sub-VI’s: Main VIs:
- 4. Results: Second Order Transfer Function Model: The second order instance generates a transfer function with the following equation: where K is the steady-state value of the response in the case of a unit step input, wn is the natural frequency, and is the damping ratio. PID Model: Proportional Gain (Kc) represents the proportional gain of the controller. In the equation that defines the PID Academic form, Kc represents the proportional gain. The default is 1. Integral Time [s] (Ti) is the controller parameter that adjusts the effect of the error integral term E(s)/s on the controller output U(s). In the equation that defines the PID Academic form, Ti represents the integral time. The default is 0. Derivative Time [s] (Td) is the controller parameter that adjusts the effect of the error derivative term sE(s) on the controller output U(s). In the equation that defines the PID Academic form, Td represents the derivative time. The default is 0. The default PID Academic controller does not use derivative time. error in describes error conditions that occur before this node runs. This input provides standard error in functionality. High Frequency Time Constant [s] (Tf) is the low pass filter time constant Tf this VI uses to make the PID model a proper system. The default is 0. Transfer Function Model returns the transfer function this VI constructs based on the inputs. To access and modify the data in the model, use the Model Information VIs. error out contains error information. This output provides standard error out functionality. Series State-Space: Two linear models are connected in series. The system models either must be continuous-time models or must have the same sampling time if they are discrete-time models. Wire data to the Model 1 and Model 2 inputs to determine the polymorphic instance to use or manually select the instance. Feedback Model: Connects two linear models in feedback configuration. The system models either must be continuous-time models or must have the same sampling time if they are discrete-time models. Wire
- 5. data to the Model 1 and Model 2 inputs to determine the polymorphic instance to use or manually select the instance. Feedback Sign specifies the sign of all feedback connections. If Feedback Sign is positive (TRUE), all feedback connections are positive. If Feedback Sign is negative (FALSE), all feedback connections are negative. The default is negative (FALSE). When you specify connections using Feedback Connections, this VI ignores Feedback Sign. Model 1 is the first model this VI uses to create the Closed-Loop Model. This model represents the system in the forward loop path. Model 2 is the second model this VI uses to create the Closed-Loop Model. This model represents the system in the feedback path. If you do not wire a model to Model 2, then this VI assumes a unit feedback by defining Model 2 as the unit gain matrix. The number of connections in Feedback Connections defines the size of the unit gain matrix. Feedback Connections uses the index number of the input and output to define each input- output pair, from Model 1 and Model 2, in a feedback loop. This VI adds or subtracts the output value of Model 1 or Model 2 from a reference input and assigns a value to the input of Model 1. Signal determines if this VI adds or subtracts the output of Model 1 to the reference input. The indexes are zero-based. If you do not specify any Feedback Connections, this VI connects as many input-output pairs as possible from Model 1 to Model 2, and Feedback Sign specifies the sign of all feedback connections. If you specify only one model, this VI feeds back the outputs from Model 1 to the inputs of Model 1. If you specify only one model and you do not specify any Feedback Connections, this VI applies unit feedback to Model 1 with as many connections as possible in ascending order. Model Output specifies the index number of the output of Model 1 or Model 2 to which you want to connect an input of Model 1 or Model 2. If you have only one model, Model Output specifies the index number of the inputs of Model 1. If you have two models, Model Output specifies the index number of the inputs of Model 2. Model 1 Input specifies the index number of the input of Model 1 to which you want to connect an output of Model 1 or Model 2. The indexes are zero-based. Signal defines the feedback sign for the connection that Model Output and Model 1 Input specify. If you define input-output pairs using Feedback Connections, this VI uses Signal to define the feedback sign instead of Feedback Sign. The default is negative. error in describes error conditions that occur before this node runs. This input provides standard error in functionality. Output Connections uses the index number of the input and output to define each input- output pair, from Model 1 and Model 2, in a feedback loop. If you do not specify any Output Connections, this VI connects as many input-output pairs as possible from Model 2 to Model 1. If you specify only one model in this VI, the VI does not use the Output Connections in feedback calculations. Model 1 Output specifies the index number of the output of Model 1 to which you want to connect an input of Model 2. Signal determines if this VI adds or subtracts the output of Model 1 to the reference input. The indexes are zero-based. Model 2 Input specifies the index number of the input of Model 2 to which you want to connect the output of Model 1. The indexes are zero-based. Signal defines the feedback sign for the connection that Model 1 Output and Model 2 Input specify. Signal specifies if this VI adds or subtracts the output of Model 1 to a reference to define the input of Model 2. The default is negative. Closed-Loop Model represents the closed-loop system that results from this VI connecting Model 1 and Model 2 according to the connections you specify. When the two input models are different model types, this VI determines the model type of the resulting model by the following model hierarchy: state-space>transfer function>zero-pole-gain. For example, if one input is a state-space model and the other is a zero-pole-gain model, the resulting model is a state-space model. To access and modify the data in the model, use the Model Information VIs. error out contains error information. This output provides standard error out functionality.
- 6. Step Response (Transfer Function): Transfer Function Model contains a mathematical representation of and information about the system of which this VI calculates step response. Initial Conditions specifies the initial values of the states or outputs. The default is 0. error in describes error conditions that occur before this node runs. This input provides standard error in functionality. Step Response Graph displays a graph that shows the forced response of the system when the forcing function is a step. For MIMO systems, this VI determines the step response by applying a step on one input at a time and letting other inputs to the system be zero. Step Response Data returns information about the step response. To access the Step Response Data, use the CD Get Time Response Data VI. Time is the uniformly-spaced time vector against which this VI plots the step response and the state trajectories. CD Parametric Time Response (Transfer Function Internal) Type of Analysis specifies the type of time response analysis this VI performs on the model. Transfer Function Model contains a mathematical representation of and information about the system of which this VI calculates parametric information. Initial Conditions are the initial values the parametric response uses. error in describes error conditions that occur before this node runs. This input provides standard error in functionality. This VI calculates rise time by performing a step response and measuring the time required for the system response to rise from the Lower percentage of the final steady-state value to the Upper percentage of the final steady-state value. If a system has a step response where the initial overshoot is in a direction opposite to that of the final steady-state value, that portion of the step response does not affect the calculation of the rise time. DC Gain (Transfer Function): Transfer Function Model contains a mathematical representation of and information about the system of which this VI determines DC gain. error in describes error conditions that occur before this node runs. This input provides standard error in functionality. DC Gain returns the steady state gain, which is the gain of the system at low frequencies. DC Gain is a 2D-array where the ijth element gives the DC gain of the system due to the ith output and jth input. error out contains error information. This output provides standard error out functionality. Get Time Response Data:
- 7. Time Response Data contains information about the time response of a model. Refer to the Details section for more information about the time response data. Time is the uniformly-spaced time vector against which this VI plots the impulse, initial, or step response and the state trajectories. States Data contains data about the time response of the states to the inputs. For transfer function and zero-pole- gain models, this array is empty. Limit Specification: Creates continuous or segmented masks in the time domain or in the frequency domain. You can use different instances of this VI to create multiple limits. Wire data to the Specification Cluster input to determine the polymorphic instance to use or manually select the instance. We specify the y-axis values in terms of numeric values and use this VI with the Limit Testing VI to do limit testing. Wire the Limit Specification VI and the Limit Testing VI in either a For Loop or a While Loop. Set Reset to FALSE, unless you want to change the limit. The following illustration shows the Limit Specification VI and the Limit Testing VI wired together in a While Loop. Precautions: To avoid hanging the user interface with front panel locking, configure all events you want a VI to handle in a single Event structure or always make sure there is only one Event structure in a loop. Additionally, make sure there is always an Event structure available to handle events as they occur.