New Application Center Additions

Classroom Tips and Techniques: Series Expansions

2009-11-05T05:00:00

Maple has the ability to provide various series expansions and their truncations, as well as complete formal series for a variety of elementary and special functions. In this month's article, we examine the relevant commands and interface devices that access these functionalities.

PID Tuning

2009-10-27T04:00:00

In this example we show how to design a PID controller for a non linear system. The system is a DC motor driving a pendulum, where the objective is to maintain the pendulum at an angle of 1 radian from the horizontal. We linearize the system at the operating point where the angle is 1, and then we use the dominant pole design technique and place dominant poles at -2-I, -2+I, and -1. We use the resulting PID controller to control the system. As a comparison, we also show the open loop uncontrolled system.

LQR Control Design for an Inverted Pendulum on a Cart System

2009-10-27T04:00:00

In this example we show how an inverted pendulum sitting on top of a cart can be controlled using an LQR controller.

Attachments: The plant.msys file is the linearized version of the plant model. This file was generated using the Linearization template attached to the model. Once the system has been linearized, the plant.msys file is used by the Linear System Worksheet template to create an LQR controller for the plant model.

Open Loop DC Motor

2009-10-27T04:00:00

This example shows an open loop model of a DC motor. This is the starting point for the example in the Getting Started Guide.

DC Motor with a PID Controller

2009-10-27T04:00:00

In this example we show how the velocity of a DC Motor can be controlled by a PID controller. Attachments: The MyMotor.msys file is the linearized version of the plant model. This file was generated using the Linearization template attached to the model. Once the system has been linearized, the MyMotor.msys file is used by the attached PID Tuning template to create the controller.

Two Way Hydraulic Cylinder

2009-10-27T04:00:00

This model demonstrates a two-way hydraulic valve that is controlled by a Boolean signal. The hydraulic pressure is used to push a hydraulic actuator that pushes a spring-damper system found in the Mechanical Load subsystem. An animation visualises the moving load.

Ackermann Steering

2009-10-27T04:00:00

Ackermann steering geometry is a geometric arrangement of linkages in the steering of a vehicle designed to solve the problem of wheels on the inside and outside turning on a different radii. A simple approximation to perfect Ackermann steering geometry may be generated by moving the steering pivot points inward so as to lie on a line drawn between the steering kingpins and the centre of the rear axle. The steering pivot points are joined by a rigid tie rod which can also be part of the steering mechanism, in the form of a rack and pinion.

Rollercoaster

2009-10-27T04:00:00

This model is an example of a rollercoaster ride, and the effects that a passenger would undergo. This model simulates a cart on an arbitrary track definition and consists of a drive train including three-phase AC motor, gearing, braking and speed controller, as well as tangential forces on the car and rider.

Mean Value Engine

2009-10-27T04:00:00

This is a model of an internal combustion engine, developed with the help of a well-known motor-cycle engine manufacturer. It provides the overall power/speed/torque output without considering details like piston motion and ignition. Typically, these models are used for engine control development, validation and testing.

It includes the throttle, intake manifold, engine power generated from the fuel combustion, and an applied load that represents the inertia of the vehicle, air drag and road losses.

Lorenz Attractor

2009-10-27T04:00:00

The Lorenz attractor, introduced by Edward Lorenz in 1963, is a three-dimensional system corresponding to the behaviour of chaotic flow. The map shows how the state of the system evolves over time in a complex, non-repeating pattern.

Lorenz derived the system model from the simplified equations of convection rolls arising in the atmosphere. This system has important implications for climate and weather prediction and other chaotic systems.

Lead Acid Battery

2009-10-27T04:00:00

This model simulates a lead acid battery driving a DC motor. The current sources are used to change the circuit switch from the battery driving the motor to the current sources driving the motor at the 6 hour mark. Then, the current sources drive the motor and recharge the battery at the 10 hour mark.

Hydraulic System with Rotary Hydraulic Actuator

2009-10-27T04:00:00

The fluid is contained in the closed loop hydraulic system such that minimal fluid is lost within the process. The system is transferring rotational energy from one source to another and is being controlled by a check valve.

Hydraulic Scissor Lift

2009-10-27T04:00:00

This model examines the mechanics of a scissor lift. A pressure source supplies liquid through the bottom leg via a spool valve that is initially open. A one-way valve prevents liquid flowing back into the sump from this leg.

This liquid actuates a hydraulic cylinder, which transforms the hydraulic energy into translational motion, actuating the hydraulic ram. Near the end of the simulation, a control signal is fed back to the spool valves which closes the bottom one and opens the top on. Fluid then drains back into the sump.

Hand Operated Hydraulic Jack

2009-10-27T04:00:00

Hydraulic jacks transmit a small mechanical force through one small hydraulic cylinder to a large hydraulic cylinder. This results in a large mechanical force exerted by the larger cylinder (due to Pascal’s principle which states that the pressure in a closed system is the same everywhere).

This model uses a hand pump to power the smaller hydraulic cylinder. A circular pipe transmits the hydraulic liquid from the smaller cylinder to the larger cylinder, with a check valve to prevent backflow. The larger cylinder lifts a load. The mass of the load can be changed to investigate the pressures generated in the hydraulic syste.

Hydraulic Cylinder Circuit with In/Out Switch Control

2009-10-27T04:00:00

A hydraulic cylinder, pushing on a mass-spring system, is actuated by a hydraulic circuit. The hydraulic circuit receives fluid from a hydraulic source through a pipe (fitted with a check valve to prevent backflow) during the extension phase, and drains fluid through another pipe during the retraction phase.

Design of a Home Heating Controller

2009-10-27T04:00:00

In this example, we are modeling a heating controller that is controlling the heat in a house. This house simulates the heat loss from the outside. The heat flow of the first and second floors are plotted.

Excavator

2009-10-27T04:00:00

This is a basic kinematic model for an excavator. The output of the simulation illustrates the reachable boundary of the bucket and a 3D animation illustrating the motion of the excavator in operation. This is a base model that can be extended to perform design development, safety verification and performance analysis.

Simple Tank with Constant Volume

2009-10-27T04:00:00

In this model, fluid flows from an infinite reservoir into a tank, where the fluid can flow out to maintain a constant volume in the tank. One plot shows the fluid flowing out of the tank, while another plot plot show the volume of the fluid, the pressure, and the volume flow rate in tank.

Mechanical Clock

2009-10-27T04:00:00

This model simulates and visualizes a mechanical clock running for one minute. There is a saved result found in Stored Results section so that you can view this 3-D simulation without needing to re-simulate the model.

Battery Startup

2009-10-27T04:00:00

This model simulates the startup of an internal combustion engine. The model is primarily divided into three parts: battery, alternator, and engine.

The battery model consists of two coupled components: A thermal component and an electrical component. The power losses in the electrical component are fed into the thermal component and cause a rise in temperature. The thermal component provides the operating temperature to the electrical component, which affects the performance of the battery.

A simple alternator model is used to simulate a typical peripheral device load and to provide a charge back into the battery.

The engine subsystem models the crankshaft, conrods and pistons, the cam shafts and valve train. This gives a detailed model of the inertial forces that the starter motor experiences during the startup cycle.