This invited feature article appeared in the MATLAB
News and Notes
Control design made faster and more effective
by Michael D. Sidman, Ph.D.
Engineers who design products for today's fiercely competitive markets must deliver high performance, high reliability designs in a timely manner. Perhaps the most important factor in achieving these goals is understanding the relative tradeoffs in a design. Assessing and minimizing design risk, especially in products that include complex electromechanical dynamics and servo controls, has never been simple. However, today's powerful computer modeling and analysis tools such as MATLAB, SIMULINK, and the MATLAB Toolboxes are now making it easier.
Many companies have discovered that it is faster, cheaper, and more effective to evaluate a new product's design performance and robustness using a detailed, customized model, instead of relying solely on the traditional method of building, coding, and testing a product in a laboratory. One example of this practice is in the design of motor and motion control models, which are used in such industries as computer peripherals, automotive, and semiconductors. These servo systems present numerous challenges in that they use a variety of motor types, require control power ranging from milliwatts to thousands of horsepower, and have bandwidths from fractions of a hertz to several kilohertz. In the computer peripherals industry, engineers are using analysis, modeling, and simulation tools such as MATLAB and SIMULINK to produce high-quality designs and reduce the need for costly hardware prototypes.
Creating a Model
Creating a model begins with analyzing a product's electromechanical dynamics, using physical principles and system identification results. Engineers can use these results directly to develop a SIMULINK block diagram, or, to simplify the process, they can use the MATLAB Symbolic Math Toolbox to translate the governing equations into a state-space form. They can then combine the SIMULINK plant model with a digital control system to correlate the closed-loop simulation results with laboratory performance. Once the product development team completes development and testing of the closed-loop model, they can use the model to quickly evaluate new ideas or to make modifications.
For example, an automotive test equipment manufacturer uses a servoed AC induction motor for high-performance motion control. The company is using a comprehensive SIMULINK model of the drive's mechanical, electrical, and digital control system dynamics to objectively compare and optimize different control techniques and system mechanics to achieve improved performance and robustness. Through simulations, engineers can explore how the system would perform under extreme conditions and evaluate component variations that are not easily duplicated in the product development lab. Because the model is parametric and easily changed, the engineers can rapidly test various what-if possibilities, including ideas for follow-on products.
simulation reveals motor speed, startup torque, and three-phase currents
Using the SIMULINK Model
The SIMULINK model includes the induction motor electrodynamics, the mechanical dynamics of the flexible mechanism to which it is coupled, the DC-link power electronics, and the digital control system. By combining the electromagnetics, the mechanics, the electronics, and controls, engineers can now observe the interaction and transient response of the complete system, including instantaneous motor current, slip frequency, electromagnetic torque, resonance excitation, and control saturation.
Modern space vector analysis techniques are used to construct a state-space model of the time-varying, nonlinear electrodynamics of the induction motor. Unlike slip-model circuit equivalents, which simulate only steady-state performance, the dynamic state-space vector model is fully responsive to both electrical and mechanical transients. For example, given the three-phase voltages applied to the stator, the model can accurately and simultaneously predict instantaneous electromagnetic rotor torque, the resulting current in each of three phases, electrical power, and the magnitude and orientation of the flux vector in one of several coordinate systems.
The model also enables engineers to add a vector controller to compare flux vector control performance for a given AC induction motor application versus standard V/F control performance. A tool like this is significant, since it allows engineers to evaluate virtually any control scheme. SIMULINK has all the capabilities to build and simulate such a complex, nonlinear, time-varying system, and then integrate it with models of a µC/DSP-based controller and an attached mechanism.
The SIMULINK simulation reveals motor speed, startup torque, and current for an unloaded induction motor connected to a fixed AC voltage supply, as shown in the graph on the previous page. The graph shows how electromagnetic torque is somewhat oscillatory after initial power-up, even with a balanced three-phase supply. Torque also achieves a maximum value prior to reaching synchronous speed, due to the torque-slip curve of an induction machine.
Designing Digital Servo Systems with MATLAB
Disk drive manufacturers can also use a fully integrated, parametric system model, with all the major plant idiosyncrasies, to evaluate new and proprietary control concepts, as well as the effect of changes to the mechanics. Such models display system performance such as seeking, tracking, shock, and vibration sensitivity, along with many dynamic variables that are otherwise unobservable in the laboratory. These models are very useful to both multidisciplinary development teams and functional design groups.
The graph at left shows SIMULINK simulation results for a small form factor magnetic disk drive. The model that produced these plots includes an optimally-designed seek velocity deceleration profile, deceleration anticipation and track following digital control, mechanical disturbances including track runout and actuator bias forces, and quantization due to D/A and A/D conversion. During the seek phase of this full-stroke seek simulation, full power supply is applied to the torque motor until it reaches a maximum allowable velocity. During deceleration, motor current is controlled by a speed loop that makes near-optimal use of the power supply and the motor. Near the destination, the servo system switches over to position mode and begins to track follow. The remaining error seen after settling is due to residual bias torque and sinusoidal track runout.
Seek and Capture
The object of disk drive servo control is to first seek and capture as quickly as possible, and then track follow as accurately as possible, despite disturbances and mechanical or electrical variations. A more complete model would include dynamics and disturbances such as actuator bearing stiction, spindle bearing induced runout, arm/actuator/flexure resonances, fixed-point arithmetic roundoff quantization, external shock and vibration, power amplifier and torque motor electrodynamics, an optimal settling algorithm, bias estimation, and automatic runout correction.
Such a model can be used to reduce seek/settling time, tune servo system parameters, predict tracking and settling errors due to the combined effect of bias forces, friction, and runout, observe operating shock and vibration sensitivity, or even determine the effect of a change in mechanics or power electronics. These models and other MATLAB-based digital servo system design tools are being used by leading disk drive manufacturers, mass storage servo chip suppliers, and test equipment suppliers.
SIMULINK has a rich set of elements that enable engineers to build complex models with dozens of states and hundreds of elements. Model development is an excellent long-term investment in a company's technology base. Assembling an encyclopedic bag of tricks is often the hallmark of a successful long-term competitor in any marketplace. Once a company has tested a comprehensive model, the incremental maintenance required to keep pace with subsequent design changes or new product designs is usually a straightforward task.
simulations are used to improve seeking and tracking
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