In August I went on holiday to Sri Lanka. During this trip I wanted to do some landscape and long exposure photographing. A tripod is really necessary for the latter. Furthermore, it was also a good excuse to myself to justify the reason to buy a tripod. However, as with any product, there are various on the market and sometimes it is difficult to find the best buy. Each one of them have different features and specifications, such as, expensive versus cheap, light versus heavy, small versus big, et cetera. As with most of the products which I buy I tried to minimize the price but maximize the features. The two most important requirements which I wanted to optimize, besides the cost, were
Minimize the weight of the tripod but ensuring the stability and endurance of the tripod
Maximize the unfolded height of the tripod but minimize the folded height
Based on those criteria you are quickly directed to the tripods which are branded in the market as travel tripods. Below a table with the tripods which I took into consideration.
Minimal height [cm]
Maximal height [cm]
Folded height [cm]
Maximum load [kg]
After balancing the advantages and disadvantages I decided to go for the MeFoto Roadtrip. For several reasons:
For one it had good reviews on the internet, one particular which I liked was the review by Jason in the YouTube video below, which I also recommend too you to watch.
The tripod was not too expensive compared to other tripods.
It had the highest unfolded height
Of all the tripods in the table above it is the heaviest, however, I considered 1.6 [kg] still as lightweight.
Because I wasn’t planning to use the tripod on a daily bases I decided that an tripod of aluminium, instead of a carbon fiber one, would be durable enough
The bar to which the camera is attached has a hook on the bottom to which extra weight can be added to increase the stability of the tripod. Along with the feature that the bar could be mounted upside down, which added to possibility to take photo’s directly at ground level. Were two features which I particularly liked.
Apart from the reasons above the MeFoto Roadtrip had also most of the features which other tripods featured, therefor the decision was made.
If you are ever looking for a reason to buy a tripod consider the following reasons:
a tripod helps when using long exposures, for instance, you will need this when doing astrophotography.
taking time lapses, panoramas, panning and videos become a lot easier since you have great support for your camera.
when using a tripod you actually think a lot more about the framing of your shot, this is because everything takes a bit longer, setting up the tripod, adjusting, et cetera.
self portraits are of a higher quality then when using a selfie stick.
In the previous blog we introduced the various types of signals present in a digital control system and highlighted the pros and cons. In this blog we take a a closer look at the digital control system.
A digital control system, can only cope with digital signals. That is because it is inherently discrete in time and space. This is caused by the processors clock rate and due to the finite word length of a digital system. For instance, a 32 [bit] computer which runs at 4 [GHz] has a time resolution of 0.25 [ns] and the value of an unsigned integer can only range from 0 to 232 − 1.
Figure 1 shows the digital control system in its most elementary form. Herein is the sampler. The sampler converts the analog output signal of the plant at time to a digital measurement signal at discrete-time . As mentioned in the previous blog, the digital signal is obtained by sampling and quantization of the analog signal. In final, denotes the recronstructor, also known as a digital-analog convertor (DAC), it converts the digital control signal provided by the controller to an analog control signal .
Figure 2 shows that the sampler exists out of two devices namely; i) a sample and hold (SH) device and ii) a analog-digtal convertor (ADC).
The SH device knows two different states. The first state is called the track state at which the analog input signal is tracked by the SH device. The track state is also refereed to as sample state. However because of the ambiguous meaning of the word sample we will use the track, which is also commonly used in literature. The second state is called the hold state at which the analog input signal is being kept constant for a short period of time. The hold state is activated when the hold command is given. During the hold state the ADC is able to process and digitize the signal. The hold command can be triggered by any logic device. While there are many more aspects and subtleties to be considered with a SH device this gives a summarized overview of its functionality.
Various different strategies exists at what time instance the hold command is triggered. These are called sampling strategies.
Periodic sampling; the sampling instances are equally spaced, that is to say with and , given in [s], being the sampling period. See also Figure 2(a). The sampling period is often also denoted as the sampling rate or sampling frequency , given in [Hz]. It is related to the sampling period by .
Multi-order sampling; a pattern of sampling instances are repeated periodically, as a result . See Figure 2(b).
Event-based sampling; the sampling instances are generated based on a event in the system. For instance, when a certain measurement threshold has been crossed. See Figure 2(c) in which the signal is sampled at every value.
Random sampling; the sampling time instances are chosen at random, see Figure 2(d).
Periodic sampling is the most common in industry. That is because of several reason; i) most deterministic behavior, ii) extensively been researched, iii) easiest to model and iv) easiest to obtain key performance indicators, for instance, in time- and frequency domain. Finally, proofing stability for the other sampling strategies is much harder then for periodic sampling.
Digital control systems never did get enough attention during my Master System & Control in my opinion. In the various courses which I was taught, continuous-time control systems were always examined, but almost never digital control systems. For most courses this is also perfectly fine. However, you would expect that there would be also a more in-depth course about digital control systems into the curriculum. Especially, since almost all control systems are a digital control system.
I remember a course in which each group had to program a robot to convey pizza’s from one cabinet to another. A group mentioned, during their presentation, that they used a PID controller to control the various axis of the robot. I knew all the groups had designed their control algorithms in the continuous-time domain, therefore I asked; i) what discretization method(s) they had used, ii) if they had check the stability and iii) if they had checked the robustness (phase, gain and modulus margin) of their digital control system with respect to the continuous-time domain controller. Unfortunately none of my questions were answered. This disappointed me and was an acknowledgement of my opinion that not enough attention was given to digital control systems. Since this was one of the last courses given before one started their internship and graduation.
For the above reason, I will do a couple of blogs about digital control systems. I will try to focus on a single topic each blog and keep it clear and easy to understand; “If you can’t explain it simply, you don’t understand it well enough.”. In this first blog I will briefly go into the pros and cons of digital control systems and its analog counterpart. Followed by the introduction of the various type of signals that are present in a digital control system.
Pros and cons of digital control systems
Below is a list of pros and cons for both digital as well as analog control systems. Remark that there might be many more and that some pros or cons are subject to opinion, experience or interpretation.
Robust; do not (often) break down
Continuous processing; no inherent bandwidth limits
Hard to modify; time-consuming, hardware needs to be rebuilt
Flexible; ability to create complicated controllers, easy to modify and fast to develop, less susceptible to aging and environmental variations
Robust; performance or safety can be monitored, errors can be dealt with appropriately
Diagnostics; on-the-fly testing, parameters can be adjusted, measurement signals can be stored
Slow development; difficult to develop accurate designs due to tolerances in components
Complex: difficult to create complicated controllers, also hard to modify, testing alternatives is difficult, hard to build in intelligence, difficult to do multi-input-multi-output control
Discrete; signal might be inaccurate due to finite word length, time delays in control loop, discrete controller, stability might be an issue
Complex; complicated controllers, difficult to obtain a high bandwidth
While analog control systems have considerable disadvantages the flexibility of digital control systems stands-out. The latter made sure that companies adopted digital over their counterpart because it opened multiply doors. For instance, the rapid development of a complex controllers which incorporated optimization algorithms to maximize performance and profit. All created at the tenth of the costs for the same analog control system.
Types of signals in a digital control systems
The main disadvantage of digital control systems is found in the fact that one has to deal with discrete variables instead of continuous ones. Consequently, let us define the different types of signals. A Continuous-time signal is a signal for which every point in the time domain, this can be infinitely, an amplitude is defined. Similarly, a discrete-time signal is a signal for which only a sequence of points in time an amplitude is defined. Note that these points in time do necessarily have to be equidistant. In case it is, the signal has an associated periodic interval. Likewise to the domain, signals may also be continuous or discrete with respect to their range, i.e., amplitude.
Summarized; in general signals can either be continuous or discrete with respect to their domain or range. Herein, the domain is in general time, in case of control systems and the range can be anything; Voltage, Amperes, Newtons, meter per second, et cetera. Figure 1 shows the four possible combinations.
In Figure 1(a) an analog signal is displayed, which is both continuous in time and amplitude. Figure 1(b) shows a sampled signal; continuous in amplitude and discrete in time; Figure 1(c) the quantized signal, discrete in amplitude and continuous in time. Finally Figure 1(d), the digital signal. This signal is both discrete in time and amplitude. Remark: the exact definition of a quantized signal and sampled signal are often ambiguous. Often it is implicitly assumed that a quantized signal is also sampled, e.g., discrete in time. Likewise, the sampled signal is sometimes in explicitly assumed to be quantized as well. Lastly, the digital signal can be obtained by sampling and quantization of the analog signal.
We have read about the pros and con, and defined the different signal types present in a digital control system. Conclusively, I want you to point to the books in the references below, these are the best literature references in this field. I also use them as a reference for these blogs, and will try to point or refer to a chapter or section from the book when addressing a certain topic. In the next blog we will focus on the different system components of a digital control system.
 Levine, William S., ed. “The Control Handbook: Control System Fundamentals”. CRC press, 2010.
 Åström, Karl J., and Björn Wittenmark. “Computer-controlled systems: theory and design”. Courier Corporation, 2013.
 Franklin, Gene F., et al. “Feedback control of dynamic systems”. Vol. 3. Reading, MA: Addison-Wesley, 1994.
 Wittenmark, Björn, Karl Johan Åström, and Karl-Erik Årzén. “Computer control: An overview”. IFAC Professional Brief, 2002.
 Ogata, K. “Discrete-Time Control Systems”. Pearson Education, 1995.
At some point one you will want to keep track of your expenses to gain insight where you can save money. There are many websites and programs which offer insight into your expenses, for instance, YouNeedABudget, MoneyDashboard, GNUCash. However, for following three main reasons I decided to simply create my own expenses spreadsheet using Microsoft Excel.
The programs often have a learning curve and you have to adapt to their way of working.
I wanted to use a tool of which I can be almost certain that it will still exist in +20 years.
Sometimes you will find yourself in the spot in which you want to have insight into some details. But, unfortunately these are not (directly) provided by the tool. Therefor I wanted to be able to program myself to gain insight. However, this still should be fairly simple to do.
Now let me tell you what my spreadsheet provides. Since I wanted to categorize my expenses I created one sheet with categories and subcategories. To keep track of all the transactions, a table was created in which all main transactions details are logged. The table has the following fields: bank account, type of account (saving or payment?), date, type (income or expense?), amount, currency, kind (variabel or fixed?), category, subcategory and remarks. While there is a currency field, it is not used yet. The with main reason for this is because fortunately I do not have to deal with money different currency types. To gain insight into the data from the table, three pivot tables and charts were created. Using the pivot tables and charts, which are semi-interactive, one is able to, for instance, zoom-in in a particular category or time stamp. To finalize, I created a kind of dashboard in which all income and expenses data is summarized per month. First details are displayed about my balance of my payment and savings account. Followed by all the expenses details, sorted by category. Using the outline group functionality one is able to open the category and list the subcategories for that month. For each category and subcategory I show its portion (in percentage) with respect to all expenses, the median per month and the average per month. Using conditional formatting this data is also visualized to give a overview, such that you are able to identify the ratios and relationships quickly. sparklines are being used to show the trend of the expenses through out the year. Concluding, the dashboard sheet makes sure that all the data and details are visible at one glance but still manages to dive into details.