Chiu H. Choi

Step Response Improvement by Pole Placement with Observer

This paper presents simulation results for improving the performance of a single-input, single-output state-space system by the method of pole placement using an estimate of the state vector generated by a full-order observer. The particular performance criteria under consideration are percent overshoot, 2% settling time, and zero steady-state error of the unit step response of the state-space system. It is observed that if the initial conditions of the observer are not close to those of the original system, the use of the observer state in place of the actual state for pole placement will result in significant deviation of the performance criteria from the desired criteria. If the initial conditions of the observer are very close to that of the state-space system, the use of the observer state can yield results close to that of using the actual state. For the case that the initial conditions of the observer are not close to those of the state-space system, there is no improvement of the performance criteria by pushing the observer poles deep into the left half plane even though this will make the state of the observer converge rapidly to the state of the original system.

Effect of observer poles on step responses

State feedback using an observer is a technique for placing the poles of a linear system at desired locations. An application of such technique is to stabilize an unstable system by placing the new system poles in the left half plane. When the desired system poles are achieved by using observer state feedback, the step response parameters such as peak time, settling time, and percent overshoot are no longer controlled by the desired dominant system poles. The observer poles can change these parameters. This paper intends to elucidate this effect through computer simulations. A set of experiments were conducted with observer poles gradually farther away from the desired system poles. With the observer poles being pushed deeper into the left half plane, the observer states can track the system state faster. It is expected that the step response parameters will be closer to those dictated by the dominant poles. But such improvement was only minimally observed in the simulation results.

Mixed-signal System-on-a-Chip (SoC) verification based on SystemVerilog model

Simulation speed and a lack of test approaches are the main difficulties in the mixed-signal verification of a complex System-on-a-Chip (SoC). In this paper, an equivalent high-level Radio Frequency (RF) model is created by the SystemVerilog language and integrated into a mixed-signal SoC. Such a model can be executed on a digital simulator, which is dramatically faster than the traditional method using an analog solver. Some mixed-signal verification approaches based on digital methods (including constrained random data generation, assertion-based verification, coverage-driven verification, and Verification Methodology Manual) are also presented as well as a case on the integrated SoC.

Applications of embedded controllers in speed and position controls

This tutorial paper presents the experimental results of solving speed and position control problems by using embedded controllers. The embedded controllers used proportional, integral, and derivative controls. A feature of these controllers is that the sample time is not explicitly included in the integral and derivative control equations. This feature was experimentally tested. In the testing of the integral control with such feature, the controller was applied to a speed regulation problem under the condition of rapidly changing load. In the testing of the derivative control with the same feature, the controller was applied to a ringing removal problem. The results were that these controllers performed as expected. Other experiments of position controls and their results were also presented. All the embedded controllers were implemented in a member of Freescale Semiconductors MC68HC12 microcontroller family

Improving the efficiency of matrix operations in the numerical solution of large implicit systems of linear differential equations

By combining techniques from numerical linear algebra and well-developed and effective software for ordinary differential equations, a package of efficient procedures has been implemented to compute the numerical solution of large implicit systems of (stiff) linear differential equations of the form without explicitly forming E −1. Such systems arise naturally in, for example, closed-loop simulations of state space models derived from finite element analysis. Numerical experiments have been run to evaluate the performance of the package with respect to accuracy and efficiency. The results showed that exploiting linearity resulted in significant time savings in the solution of high order problems. It was also observed that substantial improvement was possible even for systems of modest size.

Comparing microcontroller and analog methods for tracking control experiments

This paper describes the development of undergraduate laboratory experiments for solving tracking control problems by using two different approaches. The first approach is based on microcontrollers and the second approach is an analog approach based on operational amplifiers. The main objective is to compare by hands-on experiments the advantages and disadvantages of these two approaches. Preliminary results of the comparison are presented in this paper. These lab experiments are developed to increase the competency skills of the students rather than just an additional topic to be covered in the course. These experiments will provide guidance to the students in making better choices of tracking controllers in their future robotics or other control system design projects.

Genetic approach to pole placement in linear state space systems

This paper describes a genetic approach for shaping the dynamic responses of linear state space systems through pole placement. The genetic approach generates a gain vector K. The vector K is used in state feedback for altering the poles of the system so as to meet step response requirements such as settling time and percent overshoot. To obtain the gain vector K by the proposed genetic approach, a pair of ideal, desired poles is calculate first and the corresponding gain vector K is computed based on the desired poles. That K vector is bred and mutated into a population. Each member of the population is tested for its fitness (the degree to which it matches the criteria). A new population is created each “generation” from the results of the previous iteration, until the criteria are met, or a certain number of generations have passed. Several case studies are provided in this paper to illustrate that this new approach is working.

Reference designs for embedded controls

A set of reference designs suitable for our student design projects was developed and tested. The purpose is to make them available for students to choose the ones suitable for integration into their projects with confidence. All the reference designs are available on our website. Some of those that are intended for embedded control applications are described in this paper. They are reference designs for DC motor driver, stepper motor driver, and GPS module. These reference designs were adopted into our embedded control projects before. Other reference designs were also developed but due to limited space are not included into this paper but the hyperlinks to them are provided. Some of the interesting projects and their evaluations are also described in this paper. Another aspect of this paper is the description of the structure of the reference designs and the various issues encountered. The information should be useful to those intend to develop reference designs for their own design courses.

Improving step responses by pole placement using reduced-order observers

This work presents the results in the investigation of using reduced-order observers in satisfying step response requirements. The reduced-order observers are used to generate the unavailable states that are used in the method of pole placement for meeting the step response requirements. The step response requirements under consideration in this paper are percent overshoot, 2% settling time, and zero steady-state error. It is observed that if the initial conditions of the reduced-order observer are not close to those of the unavailable states, the use of the reduced-order observer state variables in pole placement will result in step responses not meeting the desired performance criteria. Further, there is no improvement of the performance criteria by pushing the reduced-order observer poles deep into the left half plane even though this will make the states of the reduced-order observer converge more rapidly to the unavailable states.

Design of Compensators for Meeting the Specification of Peak Value

This paper describes a method for designing a compensator that will drive the peak value of the unit step response to a specified value and will eliminate the steady-state error. This method is an iterative method. An assumption of dominant closed-loop complex poles is required. The method was simulated and the desired results were obtained.