Terminal sliding mode

Key takeaways

Terminal sliding mode belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Terminal sliding mode to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Terminal sliding mode from memory before moving on to harder problems.

Reference excerpt

In the early 1990s, a new type of sliding mode control, named terminal sliding modes (TSM) was invented at the Jet Propulsion Laboratory (JPL) by Venkataraman and Gulati. TSM is robust non-linear control approach. The main idea of terminal sliding mode control evolved out of seminal work on terminal attractors done by Zak in the JPL, and is evoked by the concept of terminal attractors which guarantee finite time convergence of the states. While, in normal sliding mode, asymptotic stability is promised which leads to the convergence of the states to the origin. But this convergence may only be guaranteed within infinite time. In TSM, a nonlinear term is introduced in the sliding surface design so that the manifold is formulated as an attractor. After the sliding surface is intercepted, the trajectory is attracted within the manifold and converges to the origin following a power rule. There are some variations of the TSM including: Non-singular TSM, Fast TSM, Terminal sliding mode also has been widely applied to nonlinear process control, for example, rigid robot control etc.. Several open questions still remain on the mathematical treatment of the system's behavior at the origin since it is non-Lipschitz.

Control Scheme Consider a continuous nonlinear system in canonical form

x ⋅ 1 ( t ) = x 2 ( t ) {\displaystyle {\overset {\cdot }{x}}_{1}(t)=x_{2}(t)} ......

x ⋅ n − 1 ( t ) = x n ( t ) {\displaystyle {\overset {\cdot }{x}}_{n-1}(t)=x_{n}(t)}

x ⋅ n ( t ) = a ( x ) + b ( x ) u ( t ) {\displaystyle {\overset {\cdot }{x}}_{n}(t)=a(x)+b(x)u(t)}

where x ( t ) ∈ R n {\displaystyle x(t)\in R^{n}} is the state vector, u ∈ R {\displaystyle u\in R} is the control input, a ( x ) {\displaystyle a(x)} and b ( x ) {\displaystyle b(x)} are nonlinear functions in x ( t ) {\displaystyle x(t)} . Then a sequence of terminal sliding surfaces can be designed as follows:

s 1 ( t ) = s ⋅ 0 ( t ) + α 1 ( t ) s 0 γ 1 ( t ) {\displaystyle s_{1}(t)={\overset {\cdot }{s}}_{0}(t)+\alpha _{1}(t)s_{0}^{\gamma _{1}}(t)}

s 2 ( t ) = s ⋅ 1 ( t ) + α 2 ( t ) s 1 γ 2 ( t ) {\displaystyle s_{2}(t)={\overset {\cdot }{s}}_{1}(t)+\alpha _{2}(t)s_{1}^{\gamma _{2}}(t)} ......

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Terminal sliding mode

Start with the simplest possible case. Write down what Terminal sliding mode claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Terminal sliding mode before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Terminal sliding mode ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Terminal sliding mode

In research: Terminal sliding mode appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Terminal sliding mode in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Terminal sliding mode is common in secondary-school and first-year university syllabi. It links to neighbouring topics Control theory, so understanding it makes those chapters shorter.
In everyday life: Look for Terminal sliding mode outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Terminal sliding mode in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Terminal sliding mode means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Terminal sliding mode out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Terminal sliding mode in simple terms?

In the early 1990s, a new type of sliding mode control, named terminal sliding modes (TSM) was invented at the Jet Propulsion Laboratory (JPL) by Venkataraman and Gulati. TSM is robust non-linear control approach.

Why does Terminal sliding mode matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Terminal sliding mode?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Terminal sliding mode.